[Pas] Probability Abstract 84

[pas at www.economia.unimi.it]

								December 30, 2004											Letter 84

Dear Colleagues,

I am happy to distribute my first Probability Abstract Service
Letter. This letter actually contains abstracts from the ArXiv
archive only but there are plans to fill the PAS archive from
different sources (like departmental working paper series)
in the near future as well as re-enable abstract submissions
directly to the PAS archive again (even if submitting to
ArXiv directly is always preferable).
The new PAS Web site, http://www.economia.unimi.it/PAS/
already exists and soon few new services will be announced.

Thanks to Chris Burdzy for the amount of work he has done
till now.

I whish you all a happy new year with a thought to the victims
of south-east asian earthquake.

Stefano M. Iacus

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2957. STEIN'S METHOD AND MINIMUM PARSIMONY DISTANCE AFTER SHUFFLES

Jason Fulman

Motivated by Bourque and Pevzner's simulation study of the parsimony 
method
for studying genome rearrangement, Berestycki and Durrett used 
techniques from
random graph theory to prove that the minimum parsimony distance after
iterating the random transposition shuffle undergoes a transition from 
Poisson
to normal behavior. This paper establishes an analogous result for 
minimum
parsimony distance after iterates of riffle shuffles or iterates of 
riffle
shuffles and cuts. The analysis is elegant and uses different tools: 
Stein's
method and generating functions. A useful technique which emerges is 
that of
making a problem more tractable by adding extra symmetry, then using 
Stein's
method to exploit the symmetry in the modified problem, and from this 
deducing
information about the original problem.


http://front.math.ucdavis.edu/math.PR/0410622

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2958. CONVERGENCE OF MARKOV PROCESSES NEAR SADDLE FIXED POINTS

Amanda G. Turner

We consider sequences of Markov processes in two dimensions whose fluid 
limit
is a stable solution of an ordinary differential equation of the form 
dx/dt =
b(x), where the linear part of b(x) has eigenvalues -mu and lambda for 
some
lambda, mu > 0. Here the processes are indexed so that the variance of 
the
fluctuations is inversely proportional to N. The simplest example 
arises from
the OK Corral gunfight model which was formulated by Williams and 
McIlroy
(1998) and studied by Kingman (1999). These processes exhibit their most
interesting behaviour at times of order log N so it is necessary to 
establish a
fluid limit that is valid for large times. We find that this limit is
inherently random and obtain its distribution. Using this, it is 
possible to
derive scaling limits for the points where these processes hit straight 
lines
through the origin, and the minimal distance from the origin that they 
can
attain. The power of N that gives the appropriate scaling somewhat 
surprisingly
turns out to be mu / 2(lamba + mu).


http://front.math.ucdavis.edu/math.PR/0412051

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2959. AN UMBRAL SETTING FOR CUMULANTS AND FACTORIAL MOMENTS

E. Di Nardo and  D. Senato

We provide an algebraic setting for cumulants and factorial moments 
through
the classical umbral calculus. Main tools are the compositional inverse 
of the
unity umbra, connected with the logarithmic power series, and a new 
umbra here
introduced, the singleton umbra. Various formulae are given expressing
cumulants, factorial moments and central moments by umbral functions.


http://front.math.ucdavis.edu/math.PR/0412052

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2960. UMBRAL NATURE OF THE POISSON RANDOM VARIABLES

E. Di Nardo and  D. Senato

Extending the rigorous presentation of the classical umbral calculus 
given by
Rota and Taylor in 1994, the so-called partition polynomials are 
interpreted
with the aim to point out the umbral nature of the Poisson random 
variables.
Among the new umbrae introduced, the main tool is the partition umbra 
that
leads also to a simple expression of the functional composition of the
exponential power series. Moreover a new short proof of the Lagrange 
inversion
formula is given.


http://front.math.ucdavis.edu/math.PR/0412054

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2961. ON RADIAL STOCHASTIC LOEWNER EVOLUTION IN MULTIPLY CONNECTED 
DOMAINS

Robert O. Bauer and  Roland M. Friedrich

We discuss the extension of radial SLE to multiply connected planar 
domains.
First, we extend Loewner's theory of slit mappings to multiply connected
domains by establishing the radial Komatu-Loewner equation, and show 
that a
simple curve from the boundary to the bulk is encoded by a motion on 
moduli
space and a motion on the boundary of the domain. Then, we show that the
vector-field describing the motion of the moduli is Lipschitz. We 
explain why
this implies that "consistent," conformally invariant random simple 
curves are
described by multidimensional diffusions, where one component is a 
motion on
the boundary, and the other component is a motion on moduli space. We 
argue
what the exact form of this diffusion is (up to a single real parameter
$\kappa$) in order to model boundaries of percolation clusters. 
Finally, we
show that this moduli diffusion leads to random non-self-crossing curves
satisfying the locality property if and only if $\kappa=6$.


http://front.math.ucdavis.edu/math.PR/0412060

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2962. GENERALIZED CAUCHY IDENTITIES, TREES AND MULTIDIMENSIONAL 
BROWNIAN  MOTIONS. PART I: BIJECTIVE PROOF OF GENERALIZED CAUCHY 
IDENTITIES

Piotr Sniady

In this series of articles we study connections between combinatorics of
multidimensional generalizations of Cauchy identity and continuous 
objects such
as multidimensional Brownian motions and Brownian bridges.
   In Part I of the series we present a bijective proof of 
multidimensional
generalizations of the Cauchy identity. Our bijection uses oriented 
planar
trees equipped with some linear orders.


http://front.math.ucdavis.edu/math.CO/0412043

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2963. THE CHROMATIC NUMBER OF RANDOM REGULAR GRAPHS

Dimitris Achlioptas and Cristopher Moore

Given any integer d >= 3, let k be the smallest integer such that d < 
2k log
k. We prove that with high probability the chromatic number of a random
d-regular graph is k, k+1, or k+2, and that if (2k-1) \log k < d < 2k 
\log k
then the chromatic number is either k+1 or k+2.


http://front.math.ucdavis.edu/cond-mat/0407278

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2964. NONNEGATIVE MATRIX FACTORIZATION AND I-DIVERGENCE ALTERNATING  
MINIMIZATION

Lorenzo Finesso and Peter Spreij

In this paper we consider the Nonnegative Matrix Factorization (NMF) 
problem:
given an (elementwise) nonnegative matrix $V \in \R_+^{m\times n}$ 
find, for
assigned $k$, nonnegative matrices $W\in\R_+^{m\times k}$ and
$H\in\R_+^{k\times n}$ such that $V=WH$. Exact, non trivial, nonnegative
factorizations do not always exist, hence it is interesting to pose the
approximate NMF problem. The criterion which is commonly employed is
I-divergence between nonnegative matrices. The problem becomes that of 
finding,
for assigned $k$, the factorization $WH$ closest to $V$ in 
I-divergence. An
iterative algorithm, EM like, for the construction of the best pair 
$(W, H)$
has been proposed in the literature. In this paper we interpret the 
algorithm
as an alternating minimization procedure \`a la Csisz\'ar-Tusn\'ady and
investigate some of its stability properties. NMF is widespreading as a 
data
analysis method in applications for which the positivity constraint is
relevant. There are other data analysis methods which impose some form 
of
nonnegativity: we discuss here the connections between NMF and 
Archetypal
Analysis.


http://front.math.ucdavis.edu/math.OC/0412070

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2965. RANDOM PARTITIONS APPROXIMATING THE COALESCENCE OF LINEAGES 
DURING A  SELECTIVE SWEEP

Jason Schweinsberg and Rick Durrett

When a beneficial mutation occurs in a population, the new, favored 
allele
may spread to the entire population. This process is known as a 
selective
sweep. Suppose we sample $n$ individuals at the end of a selective 
sweep. If we
focus on a site on the chromosome that is close to the location of the
beneficial mutation, then many of the lineages will likely be descended 
from
the individual that had the beneficial mutation, while others will be 
descended
from a different individual because of recombination between the two 
sites. We
introduce two approximations for the effect of a selective sweep. The 
first one
is simple but not very accurate: flip $n$ independent coins with 
probability
$p$ of heads and say that the lineages whose coins come up heads are 
those that
are descended from the individual with the beneficial mutation. A second
approximation, which is related to Kingman's paintbox construction, 
replaces
the coin flips by integer-valued random variables and leads to very 
accurate
results.


http://front.math.ucdavis.edu/math.PR/0411069

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2966. ON SKOROHOD SPACES AS UNIVERSAL SAMPLE PATH SPACES

Oliver Delzeith

The paper presents a factorization theorem for a certain class of 
stochastic
processes. Skorohod spaces carry the rich structure of standard Borel 
spaces
and appear to be suitable universal sample path spaces. We show that, 
if $\xi$
is a RCLL stochastic process with values in a complete separable metric 
space
$E$, any other RCLL stochastic process $X$ adapted to the filtration 
induced by
$\xi$ factors through the Skorohod space $D_E[0,\infty)$. This can be
understood as an extension of a stochastic process to a standard Borel 
space
enjoying nice properties. Moreover, the trajectories of the factorized
stochastic process defined on $D_E[0,\infty)$ inherit the properties of 
being
continuous, non-decreasing, and of bounded variation, resp., from those 
of $X$.
   Considering situations which are invariant under the factorization 
procedure,
the main theorem is a reduction tool to assume the underlying 
measurable space
be a standard Borel space. In an example, we pick the existence theorem 
of
regular conditional probabilities on standard Borel spaces to simplify a
conditional expectation appearing in stochastic control problems.


http://front.math.ucdavis.edu/math.PR/0412092

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2967. A MASS TRANSFERENCE PRINCIPLE AND THE DUFFIN-SCHAEFFER CONJECTURE 
FOR  HAUSDORFF MEASURES

Victor Beresnevich and Sanju Velani

A Hausdorff measure version of the Duffin-Schaeffer conjecture in metric
number theory is introduced and discussed. The general conjecture is
established modulo the original conjecture. The key result is a Mass
Transference Principle which allows us to transfer Lebesgue measure 
theoretic
statements for $\limsup$ subsets of $\R^k$ to Hausdorff measure 
theoretic
statements. In view of this, the Lebesgue theory of $\limsup $ sets is 
shown to
underpin the general Hausdorff theory. This is rather surprising since 
the
latter theory is viewed to be a subtle refinement of the former.


http://front.math.ucdavis.edu/math.NT/0412141

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2968. DESTRUCTION OF VERY SIMPLE TREES

James Allen Fill and  Nevin Kapur and  Alois Panholzer

We consider the total cost of cutting down a random rooted tree chosen 
from a
family of so-called very simple trees (which include ordered trees, 
$d$-ary
trees, and Cayley trees); these form a subfamily of simply generated 
trees. At
each stage of the process an edge is chose at random from the tree and 
cut,
separating the tree into two components. In the one-sided variant of the
process the component not containing the root is discarded, whereas in 
the
two-sided variant both components are kept. The process ends when no 
edges
remain for cutting. The cost of cutting an edge from a tree of size $n$ 
is
assumed to be $n^\alpha$. Using singularity analysis and the method of 
moments,
we derive the limiting distribution of the total cost accrued in both 
variants
of this process. A salient feature of the limiting distributions 
obtained
(after normalizing in a family-specific manner) is that they only 
depend on
$\alpha$.


http://front.math.ucdavis.edu/math.PR/0412155

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2969. RANDOM PARTITIONING PROBLEMS INVOLVING POISSON POINT PROCESSES ON 
THE  INTERVAL

Thierry Huillet (LPTM)

Suppose some random resource (energy, mass or space) $\chi \geq 0$ is 
to be
shared at random between (possibly infinitely many) species (atoms or
fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the 
amount of
the individual share is necessarily bounded from above by 1. This random
partitioning model can naturally be identified with the study of 
infinitely
divisible random variables with L\'{e}vy measure concentrated on the 
interval%
$.$ Special emphasis is put on these special partitioning models in the
Poisson-Kingman class. The masses attached to the atoms of such 
partitions are
sorted in decreasing order. Considering nearest- neighbors spacings 
yields a
partition of unity which also deserves special interest. For such 
partition
models, various statistical questions are addressed among which: 
correlation
structure, cumulative energy of the first $K$ largest items, partition
function, threshold and covering statistics, weighted partition, 
R\'{e}nyi's,
typical and size-biased fragments size. Several physical images are 
supplied.
When the unbounded L\'{e}vy measure of $\chi $ is $\theta x^{-1}\cdot 
{\bf I}%
(x\in (0,1)) dx$, the spacings partition has Griffiths-Engen-McCloskey 
or
GEM$(\theta) $ distribution and $% \chi $ follows Dickman distribution. 
The
induced partition models have many remarkable peculiarities which are 
outlined.
The case with finitely many (Poisson) fragments in the partition law is 
also
briefly addressed. Here, the L\'{e}vy measure is bounded.


http://front.math.ucdavis.edu/cond-mat/0412166

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2970. DEVROYE INEQUALITY FOR A CLASS OF NON-UNIFORMLY HYPERBOLIC 
DYNAMICAL  SYSTEMS

J.-R. Chazottes and  P. Collet and  B. Schmitt

In this paper, we prove an inequality, which we call "Devroye 
inequality",
for a large class of non-uniformly hyperbolic dynamical systems (M,f). 
This
class, introduced by L.-S. Young, includes families of piece-wise 
hyperbolic
maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas),
unimodal and H{\'e}non-like maps. Devroye inequality provides an upper 
bound
for the variance of observables of the form K(x,f(x),...,f^{n-1}(x)), 
where K
is any separately Holder continuous function of n variables. In 
particular, we
can deal with observables which are not Birkhoff averages. We will show 
in
\cite{CCS} some applications of Devroye inequality to statistical 
properties of
this class of dynamical systems.


http://front.math.ucdavis.edu/math.DS/0412166

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2971. STATISTICAL CONSEQUENCES OF DEVROYE INEQUALITY FOR PROCESSES.  
APPLICATIONS TO A CLASS OF NON-UNIFORMLY HYPERBOLIC DYNAMICAL SYSTEMS

J.-R. Chazottes and  P. Collet and  B. Schmitt

In this paper, we apply Devroye inequality to study various statistical
estimators and fluctuations of observables for processes. Most of these
observables are suggested by dynamical systems. These applications 
concern the
co-variance function, the integrated periodogram, the correlation 
dimension,
the kernel density estimator, the speed of convergence of empirical 
measure,
the shadowing property and the almost-sure central limit theorem. We 
proved in
\cite{CCS} that Devroye inequality holds for a class of non-uniformly
hyperbolic dynamical systems introduced in \cite{young}. In the second 
appendix
we prove that, if the decay of correlations holds with a common rate 
for all
pairs of functions, then it holds uniformly in the function spaces. In 
the last
appendix we prove that for the subclass of one-dimensional systems 
studied in
\cite{young} the density of the absolutely continuous invariant measure 
belongs
to a Besov space.


http://front.math.ucdavis.edu/math.DS/0412167

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2972. THE FOREGOUND-BACKGROUND PROCESSOR SHARING QUEUE: AN OVERVIEW

Misja Nuyens

We give an overview of the results in the literature on single-server 
queues
with the FB discipline. The FB discipline gives service to the customer 
that
has received the least amount of service. This not so well-known 
discipline has
some appealing features, and performs well for heavy-tailed service 
times. We
describe results on the queue length, sojourn time, and the influence of
variability in the service times.


http://front.math.ucdavis.edu/math.PR/0412182

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2973. A PROBABILISTIC ANALYSIS OF SOME TREE ALGORITHMS

Hanene Mohamed (RAP UR-R) and  Philippe Robert (RAP UR-R)

In this paper a general class of tree algorithms is analyzed. It is 
shown
that, by using an appropriate probabilistic representation of the 
quantities of
interest, the asymptotic behavior of these algorithms can be obtained 
quite
easily without resorting to complex analysis techniques as it is 
usually the
case. This approach gives a unified probabilistic treatment of these 
questions.
It simplifies and extends some of the results known in this domain.


http://front.math.ucdavis.edu/math.PR/0412188

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2974. A CONTINUOUS STOCHASTIC MATURATION MODEL

Djalil Chafai (LSProba and  Upte Umr Inra/Envt 181) and  Didier 
Concordet  (LSProba, Upte Umr Inra/Envt 181)

We present a continuous time model of maturation and survival, obtained 
as
the limit of a compartmental evolution model when the number of 
compartments
tends to infinity. We establish in particular an explicit formula for 
the law
of the system output under inhomogeneous killing and when the input 
follows a
time-inhomogeneous Poisson process. Identifiability issues are 
discussed, and
an application to the modelling of the toxicity of anti-cancer drugs is 
given.
Such models can be seen in particular as generalisations of previous 
works of
Jacquez & Simon and Schuhmacher & Thieme.


http://front.math.ucdavis.edu/math.PR/0412193

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2975. ON LOCAL MARTINGALE AND ITS SUPREMUM: HARMONIC FUNCTIONS AND 
BEYOND

Jan Obloj (PMA and  Mimuw) and  Marc Yor (PMA)

We discuss certain facts involving a continuous local martingale $N$ 
and its
supremum $\bar{N}$. A complete characterization of 
$(N,\bar{N})$-harmonic
functions is proposed. This yields an important family of martingales, 
the
usefulness of which is demonstrated, by means of examples involving the
Skorokhod embedding problem, bounds on the law of the supremum, or the 
local
time at 0, of a martingale with a fixed terminal distribution, or yet 
in some
Brownian penalization problems. In particular we obtain new bounds on 
the law
of the local time at 0, which involve the excess wealth order.


http://front.math.ucdavis.edu/math.PR/0412196

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2976. A COALESCENT MODEL FOR THE EFFECT OF ADVANTAGEOUS MUTATIONS ON 
THE  GENEALOGY OF A POPULATION

Rick Durrett and Jason Schweinsberg

When an advantageous mutation occurs in a population, the favorable 
allele
may spread to the entire population in a short time, an event known as a
selective sweep. As a result, when we sample $n$ individuals from a 
population
and trace their ancestral lines backwards in time, many lineages may 
coalesce
almost instantaneously at the time of a selective sweep. We show that 
as the
population size goes to infinity, this process converges to a coalescent
process called a coalescent with multiple collisions. A better 
approximation
for finite populations can be obtained using a coalescent with 
simultaneous
multiple collisions. We also show how these coalescent approximations 
can be
used to get insight into how beneficial mutations affect the behavior of
statistics that have been used to detect departures from the usual 
Kingman's
coalescent.


http://front.math.ucdavis.edu/math.PR/0411071

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2977. ROUGHENING AND INCLINATION OF COMPETITION INTERFACES

Pablo A. Ferrari and  James B. Martin and  Leandro P. R. Pimentel

The competition interface between two growing ``Young clusters'' 
(diagrams),
in a two-dimensional random cone, is mapped to the path of a 
second-class
particle in the one-dimensional totally asymmetric simple exclusion 
process.
Using the asymptotics of the second class particle and hydrodynamic 
limits for
the exclusion process (Burgers equation), we show that the behavior of 
the
competition interface depends on the angle of the cone: for angles in 
[180^o,
270^o) the competition interface has a deterministic inclination, while 
for
angles in [90^o,180^o) the inclination is random. We relate the 
competition
model to a model of random directed polymers, and obtain some partial 
results
for the fluctuations of the competition interface.


http://front.math.ucdavis.edu/math.PR/0412198

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2978. LARGE DEVIATIONS FOR ROUGH PATHS OF THE FRACTIONAL BROWNIAN MOTION

Annie Millet and  Marta Sanz-Sol\'e

Starting from the construction of a geometric rough path associated 
with a
fractional Brownian motion with Hurst parameter $H\in]{1/4}, {1/2}[$ 
given by
Coutin and Qian (2002), we prove a large deviation principle in the 
space of
geometric rough paths, extending classical results on Gaussian 
processes. As a
by-product, geometric rough paths associated to elements of the 
reproducing
kernel Hilbert space of the fractional Brownian motion are obtained and 
an
explicit integral representation is given.


http://front.math.ucdavis.edu/math.PR/0412200

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2979. ANALYTICAL PROBABILISTIC APPROACH TO THE GROUND STATE OF LATTICE 
QUANTUM

Massimo Ostilli and  Carlo Presilla

We present a large deviation analysis of a recently proposed 
probabilistic
approach to the study of the ground-state properties of lattice quantum
systems. The ground-state energy, as well as the correlation functions 
in the
ground state, are exactly determined as a series expansion in the 
cumulants of
the multiplicities of the potential and hopping energies assumed by the 
system
during its long-time evolution. Once these cumulants are known, even at 
a
finite order, our approach provides the ground state analytically as a 
function
of the Hamiltonian parameters. A scenario of possible applications of 
this
analyticity property is discussed.


http://front.math.ucdavis.edu/cond-mat/0412157

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2980. THE COMPACT SUPPORT PROPERTY FOR MEASURE-VALUED DIFFUSIONS

Ross G. Pinsky

The purpose of this article is to give a rather thorough understanding 
of the
compact support property for measure-valued diffusion processes 
corresponding
to semi-linear equations of the form \[& u_t=Lu+\beta u-\alpha u^p 
\text{in}
R^d\times (0,\infty), p\in(1,2]; &u(x,0)=f(x) \text{in} R^d; &u(x,t)\ge0
\text{in} R^d\times[0,\infty). \] In particular, we shall investigate 
how the
interplay between the underlying motion (the diffusion process 
corresponding to
$L$) and the branching affects the compact support property. In 
\cite{EP99},
the compact support property was shown to be equivalent to a certain 
analytic
criterion concerning uniqueness of the Cauchy problem for the semilinear
parabolic equation related to the measured valued diffusion. In a 
subsequent
paper \cite{EP03}, this analytic property was investigated purely from 
the
point of view of partial differential equations. Some of the results 
obtained
in this latter paper yield interesting results concerning the compact 
support
property. In this paper, the results from \cite{EP03} that are relevant 
to the
compact support property are presented, sometimes with extensions. These
results are interwoven with new results and some informal heuristics. 
Taken
together, they yield a fairly comprehensive picture of the compact 
support
property. \it Inter alia\rm, we show that the concept of a 
measure-valued
diffusion \it hitting\rm a point can be investigated via the compact 
support
property, and suggest an alternate proof of a result concerning the 
hitting of
points by super-Brownian motion.


http://front.math.ucdavis.edu/math.PR/0412246

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2981. EXPLICIT CHARACTERIZATION OF THE SUPER-REPLICATION STRATEGY IN 
FINANCIAL  MARKETS WITH PARTIAL TRANSACTION COSTS

Imen Bentahar (CEREMADE) and  Bruno Bouchard (CREST and  Lfa and  Pma)

We consider a multivariate financial market with transaction costs and 
study
the problem of finding the minimal initial capital needed to hedge, 
without
risk, European-type contingent claims. The model is similar to the one
considered in Bouchard and Touzi (2000), except that some of the assets 
can be
exchanged freely, i.e. without paying transaction costs. In this 
context, we
generalize the result of the above paper and prove that the value of 
this
stochastic control problem is given by the cost of the cheapest hedging
strategy in which the number of non-freely exchangeable assets is kept 
constant
over time.


http://front.math.ucdavis.edu/math.PR/0412247

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2982. ON AUTOMORPHISMS OF TYPE II ARVESON SYSTEMS (PROBABILISTIC 
APPROACH)

Boris Tsirelson

A counterexample to the conjecture that the automorphisms of an 
arbitrary
Arveson system act transitively on its normalized units.


http://front.math.ucdavis.edu/math.OA/0411062

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2983. MINIMAL SPANNING FORESTS

Russell Lyons and  Yuval Peres and  and Oded Schramm

We study minimal spanning forests in infinite graphs, which are weak 
limits
of minimal spanning trees from finite subgraphs corresponding to i.i.d. 
random
labels on the edges. These limits can be taken with free or wired 
boundary
conditions, and are denoted $\fmsf$ (free minimal spanning forest) and 
$\wmsf$
(wired minimal spanning forest), respectively. The $\wmsf$ is the union 
of the
trees that arise from invasion percolation started at all vertices. We 
show
that on any Cayley graph where critical percolation has no infinite 
clusters,
all the component trees in the $\wmsf$ have one end a.s. In $\Z^d$ this 
was
proved by \ref b.Alexander:MSF/, but a different method is needed for 
the
nonamenable case. We show that on any connected graph, the union of the 
$\fmsf$
and independent Bernoulli percolation (with arbitrarily small 
parameter) is
a.s. connected. In conjunction with a recent result of Gaboriau, this 
implies
that in any Cayley graph, the expected degree of the $\fmsf$ is at 
least the
expected degree of the $\fsf$ (the weak limit of uniform spanning 
trees). We
show that on any graph, each component tree in the $\wmsf$ has $\pc = 
1$ a.s.,
where $\pc$ denotes the critical probability for having an infinite 
cluster in
Bernoulli percolation. We show that the number of infinite clusters for
Bernoulli($\pu$) percolation is at most the number of components of the
$\fmsf$, where $\pu$ denotes the critical probability for having a 
unique
infinite cluster.


http://front.math.ucdavis.edu/math.PR/0412263

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2984. EMPIRICAL PROCESSES OF DEPENDENT RANDOM VARIABLES

Wei Biao Wu

Empirical processes for stationary, causal sequences are considered. We
establish empirical central limit theorems for classes of indicators of 
left
half lines, absolutely continuous functions and piecewise differentiable
functions. Sample path properties of empirical distribution functions 
are also
discussed. The results are applied to linear processes and Markov 
chains.


http://front.math.ucdavis.edu/math.ST/0412267

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2985. M-ESTIMATION OF LINEAR MODELS WITH DEPENDENT ERRORS

Wei Biao Wu

We study the asymptotic behavior of M-estimates of regression 
parameters in
multiple linear models where errors are dependent random variables. A 
Bahadur
representation of the M-estimates is derived and a central limit 
theorem is
established. The results are applied to linear models with errors being
short-range dependent linear processes, heavy-tailed linear processes 
and some
widely used nonlinear time series.


http://front.math.ucdavis.edu/math.ST/0412268

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2986. STATIONARY TRANSFORMATION OF INTEGRATED BROWNIAN MOTION

Eugene Wong

Consider an n-fold integrated Brownian motion. We show that a simple 
change
in time and scale transforms it into a stationary Gaussian process. The
collection of stationary processes so constructed not only constitutes 
an
interesting family of processes, but their spectral representation is 
also
useful in dealing with integrated Brownian motion. We illustrate this by
deriving an explicit representation for the joint density function for 
a family
of integrated Brownian motions and showing some of its properties.


http://front.math.ucdavis.edu/math.PR/0412291

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2987. NARROW ESCAPE, PART I

A. Singer and  Z. Schuss and  D. Holcman and  R.S. Eisenberg

A Brownian particle with diffusion coefficient $D$ is confined to a 
bounded
domain of volume $V$ in $\rR^3$ by a reflecting boundary, except for a 
small
absorbing window. The mean time to absorption diverges as the window 
shrinks,
thus rendering the calculation of the mean escape time a singular 
perturbation
problem. We construct an asymptotic approximation for the case of an 
elliptical
window of large semi axis $a\ll V^{1/3}$ and show that the mean escape 
time is
$E\tau\sim\ds{\frac{V}{2\pi Da}} K(e)$, where $e$ is the eccentricity 
of the
ellipse; and $K(\cdot)$ is the complete elliptic integral of the first 
kind. In
the special case of a circular hole the result reduces to Lord 
Rayleigh's
formula $E\tau\sim\ds{\frac{V}{4aD}}$, which was derived by heuristic
considerations. For the special case of a spherical domain, we obtain 
the
asymptotic expansion $E\tau=\ds{\frac{V}{4aD}} [1+\frac{a}{R} \log 
\frac{R}{a}
+ O(\frac{a}{R}) ]$. This problem is important in understanding the 
flow of
ions in and out of narrow valves that control a wide range of 
biological and
technological function.


http://front.math.ucdavis.edu/math-ph/0412048

---------------------------------------------------------------

2988. NARROW ESCAPE, PART II: THE CIRCULAR DISK

A. Singer and  Z. Schuss and  D. Holcman

We consider Brownian motion in a circular disk $\Omega$, whose boundary
$\p\Omega$ is reflecting, except for a small arc, $\p\Omega_a$, which is
absorbing. As $\epsilon=|\partial \Omega_a|/|\partial \Omega|$ 
decreases to
zero the mean time to absorption in $\p\Omega_a$, denoted $E\tau$, 
becomes
infinite. The narrow escape problem is to find an asymptotic expansion 
of
$E\tau$ for $\epsilon\ll1$. We find the first two terms in the 
expansion and an
estimate of the error. The results are extended in a straightforward 
manner to
planar domains and two-dimensional Riemannian manifolds that can be 
mapped
conformally onto the disk. Our results improve the previously derived 
expansion
for a general smooth domain, $E\tau =
\ds{\frac{|\Omega|}{D\pi}}[\log\ds{\frac{1}{\epsilon}}+O(1)],$ ($D$ is 
the
diffusion coefficient) in the case of a circular disk. We find that the 
mean
first passage time from the center of the disk is $E[\tau |
\x(0)=\mb{0}]=\ds{\frac{R^2}{D}}[\log\ds{\frac{1}{\epsilon}} + \log 2
+\ds{{1/4}} + O(\epsilon)]$. The second term in the expansion is needed 
in real
life applications, such as trafficking of receptors on neuronal spines, 
because
$\log\ds{\frac{1}{\epsilon}}$ is not necessarily large, even when 
$\epsilon$ is
small. We also find the singular behavior of the probability flux 
profile into
$\p\Omega_a$ at the endpoints of $\p\Omega_a$, and find the value of 
the flux
near the center of the window.


http://front.math.ucdavis.edu/math-ph/0412050

---------------------------------------------------------------

2989. NARROW ESCAPE, PART III: RIEMANN SURFACES AND NON-SMOOTH DOMAINS

A. Singer and  Z. Schuss and  D. Holcman

We consider Brownian motion in a bounded domain $\Omega$ on a 
two-dimensional
Riemannian manifold $(\Sigma,g)$. We assume that the boundary 
$\p\Omega$ is
smooth and reflects the trajectories, except for a small absorbing arc
$\p\Omega_a\subset\p\Omega$. As $\p\Omega_a$ is shrunk to zero the 
expected
time to absorption in $\p\Omega_a$ becomes infinite. The narrow escape 
problem
consists in constructing an asymptotic expansion of the expected 
lifetime,
denoted $E\tau$, as $\epsilon=|\partial \Omega_a|_g/|\partial 
\Omega|_g\to0$.
We derive a leading order asymptotic approximation $E\tau =
\ds{\frac{|\Omega|_g}{D\pi}}[\log\ds{\frac{1}{\epsilon}}+O(1)]$. The 
order 1
term can be evaluated for simply connected domains on a sphere by 
projecting
stereographically on the complex plane and mapping conformally on a 
circular
disk. It can also be evaluated for domains that can be mapped 
conformally onto
an annulus. This term is needed in real life applications, such as 
trafficking
of receptors on neuronal spines, because $\log\ds{\frac{1}{\epsilon}}$ 
is not
necessarily large, even when $\epsilon$ is small. If the absorbing 
window is
located at a corner of angle $\alpha$, then $E\tau =
\ds{\frac{|\Omega|_g}{D\alpha}}[\log\ds{\frac{1}{\epsilon}}+O(1)],$ if 
near a
cusp, then $E\tau$ grows algebraically, rather than logarithmically. 
Thus, in
the domain bounded between two tangent circles, the expected lifetime 
is $E\tau
= \ds{\frac{|\Omega|}{(d^{-1}-1)D}}(\frac{1}{\epsilon} + O(1))$.


http://front.math.ucdavis.edu/math-ph/0412051

---------------------------------------------------------------

2990. OPTIMAL MASS TRANSPORTATION AND MATHER THEORY

Patrick Bernard (IF) and  Boris Buffoni (EPFL)

We study optimal transportation of measures on compact manifolds for 
costs
defined from convex Lagrangians. We prove that optimal transportation 
can be
interpolated by measured Lipschitz laminations, or geometric currents. 
The
methods are inspired from Mather theory on Lagrangian systems. We make 
use of
viscosity solutions of the associated Hamilton-Jacobi equation in the 
spirit of
Fathi's approach to Mather theory.


http://front.math.ucdavis.edu/math.DS/0412299

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2991. SOME CONNECTIONS BETWEEN (SUB)CRITICAL BRANCHING MECHANISMS AND  
BERNSTEIN FUNCTIONS

Jean Bertoin (PMA) and  Bernard Roynette (IEC) and  Marc Yor (PMA)

We describe some connections, via composition, between two functional 
spaces:
the space of (sub)critical branching mechanisms and the space of 
Bernstein
functions. The functions ${\bf e}_\alpha: x\to x^{\alpha}$ where 
$x\geq0$ and
$0<\alpha\leq 1/2$, and in particular the critical parameter 
$\alpha=1/2$, play
a distinguished role.


http://front.math.ucdavis.edu/math.PR/0412322

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2992. AN URN MODEL OF DIACONIS

David Siegmund and Benjamin Yakir

An urn model of Diaconis and some generalizations are discussed. A
convergence theorem is proved that implies for Diaconis' model that the
empirical distribution of balls in the urn converges with probability 
one to
the uniform distribution.


http://front.math.ucdavis.edu/math.PR/0412333

---------------------------------------------------------------

2993. UNIFORM LARGE DEVIATIONS FOR THE NONLINEAR SCHRODINGER EQUATION 
WITH  MULTIPLICATIVE NOISE

Eric Gautier (IRMAR and  Crest-Insee Laboratoire De Statistique)

Uniform large deviations for the laws of the paths of the solutions of 
the
stochastic nonlinear Schrodinger equation when the noise converges to 
zero are
presented. The noise is a real multiplicative Gaussian noise. It is 
white in
time and colored in space. The path space considered allows blow-up and 
is
endowed with a topology analogue to a projective limit topology. Thus a 
large
variety of large deviation principle may be deduced by contraction. As a
consequence, asymptotics of the tails of the law of the blow-up time 
when the
noise converges to zero are obtained.


http://front.math.ucdavis.edu/math.AP/0412319

---------------------------------------------------------------

2994. ON FINITE RANGE STABLE TYPE CONCENTRATION

J.C. Breton and  C. Houdr\'e

The purpose of these notes is to further complete our understanding of 
the
stable concentration phenomenon, by obtaining the finite range behavior 
of
$P(F-E[F]\geq x)$, with $F=f(X)$ where $f$ is a Lipschitz function and 
$X$ is a
stable random vector or with $F$ a stochastic functional on the Poisson 
space
equipped with a stable L\'evy measure.


http://front.math.ucdavis.edu/math.PR/0412334

---------------------------------------------------------------

2995. CONSTRUCTION OF THE THERMODYNAMIC LIMIT MEASURE FOR THE PARKING 
PROCESS  AND OTHER EXCLUSION SCHEMES ON $\MATHBB{Z}^{D}$

Thomas Logan Ritchie

We provide an explicit construction for the thermodynamic limit measure 
for
finite range exclusion schemes on $\mathbb{Z}^{d}$. By means thereof a 
strong
law of large numbers for occupation densities is accomplished, and, 
amongst
other results, the so called ``super-exponential'' (i.e. gamma) decay of
pair-correlation functions is established.


http://front.math.ucdavis.edu/math.PR/0412343

---------------------------------------------------------------

2996. DIMENSION FREE AND INFINITE VARIANCE TAIL ESTIMATES ON POISSON 
SPACE

J.C. Breton and  C. Houdr\'e and  N. Privault

Concentration inequalities are obtained on Poisson space, for random
functionals with finite or infinite variance. In particular, dimension 
free
tail estimates and exponential integrability results are given for the
Euclidean norm of vectors of independent functionals.
  In the finite variance case these results are applied to infinitely 
divisible
random variables such as quadratic Wiener functionals, including 
L\'evy's
stochastic area and the square norm of Brownian paths.
  In the infinite variance case, various tail estimates such as stable 
ones are
also presented.


http://front.math.ucdavis.edu/math.PR/0412346

---------------------------------------------------------------

2997. IMPROVED LOWER BOUNDS FOR THE CRITICAL PROBABILITY OF 
ORIENTED-BOND  PERCOLATION IN TWO DIMENSIONS

Thomas Logan Ritchie and  Vladimir Belitsky

We present a coupled decreasing sequence of random walks on $ \mathbb Z 
$
that dominates the edge process of oriented-bond percolation in two 
dimensions.
Using the concept of "random walk in a strip ", we construct an 
algorithm that
generates an increasing sequence of lower bounds that converges to the 
critical
probability of oriented-bond percolation. Numerical calculations of the 
first
ten lower bounds thereby generated lead to an improved,i.e. higher, 
rigorous
lower bound to this critical probability, viz. $p_{c} \geq 0.63328 $. 
Finally a
computer simulation technique is presented; the use thereof establishes 
0.64450
as a non-rigorous five-digit-precision (lower) estimate for $p_{c}$.


http://front.math.ucdavis.edu/math.PR/0412348

---------------------------------------------------------------

2998. Q-MARKOV RANDOM PROBABILITY MEASURES AND THEIR POSTERIOR 
DISTRIBUTIONS

Raluca Balan

In this paper, we use the Markov property introduced in Balan and 
Ivanoff (J.
Theor. Probab. 15, 2002, 553-588) for set-indexed processes and we 
prove that a
Markov prior distribution leads to a Markov posterior distribution. In
particular, by proving that a neutral to the right prior distribution 
leads to
a neutral to the right posterior distribution, we extend a fundamental 
result
of Doksum (Ann. Probab. 2,1974, 183-201) to arbitrary sample spaces.


http://front.math.ucdavis.edu/math.PR/0412349

---------------------------------------------------------------

2999. A MARKOV PROPERTY FOR SET-INDEXED PROCESSES

Raluca Balan and Gail Ivanoff

We consider a type of Markov property for set-indexed processes which is
satisfied by all processes with independent increments and which allows 
us to
introduce a transition system theory leading to the construction of the
process. A set-indexed generator is defined such that it completely
characterizes the distribution of the process.


http://front.math.ucdavis.edu/math.PR/0412350

---------------------------------------------------------------

3000. STEIN ESTIMATION FOR INFINITELY DIVISIBLE LAWS

R. Averkamp and  C. Houdr\'e

Unbiased risk estimation, \`a la Stein, is studied for infinitely 
divisible
laws with finite second moment.


http://front.math.ucdavis.edu/math.ST/0412345

---------------------------------------------------------------

3001. NONPARAMETRIC ESTIMATION FOR LEVY PROCESSES WITH A VIEW TOWARDS  
MATHEMATICAL FINANCE

Enrique Figueroa-Lopez and Christian Houdre

Nonparametric methods for the estimation of the Levy density of a Levy
process are developed. Estimators that can be written in terms of the 
``jumps''
of the process are introduced, and so are discrete-data based 
approximations. A
model selection approach made up of two steps is investigated. The 
first step
consists in the selection of a good estimator from a linear model of 
proposed
Levy densities, while the second is a data-driven selection of a linear 
model
among a given collection of linear models. By providing lower bounds 
for the
minimax risk of estimation over Besov Levy densities, our estimators 
are shown
to achieve the ``best'' rate of convergence. A numerical study for the 
case of
histogram estimators and for variance Gamma processes, models of key 
importance
in risky asset price modeling driven by Levy processes, is presented.


http://front.math.ucdavis.edu/math.ST/0412351

---------------------------------------------------------------

3002. IMPROVING ON BOLD PLAY WHEN THE GAMBLER IS RESTRICTED

Jason Schweinsberg

Suppose a gambler starts with a fortune in (0,1) and wishes to attain a
fortune of 1 by making a sequence of bets. Assume thay whenever the 
gambler
stakes the amount s, the gambler's fortune increases by s with 
probability w
and decreases by s with probability 1 - w, where w < 1/2. Dubins and 
Savage
showed that the optimal strategy, which they called "bold play", is 
always to
stake min{f, 1-f}, where f is the gambler's current fortune. Here we 
consider
the problem in which the gambler may stake no more than l at one time. 
We show
that the bold strategy of always betting min{l, f, 1-f} is not optimal 
if l is
irrational, extending a result of Heath, Pruitt, and Sudderth.


http://front.math.ucdavis.edu/math.PR/0412362

---------------------------------------------------------------

3003. A GUE CENTRAL LIMIT THEOREM AND UNIVERSALITY OF DIRECTED FIRST 
AND LAST  PASSAGE SITE PERCOLATION

Jinho Baik and Toufic M. Suidan

We prove a GUE central limit theorem for random variables with finite 
fourth
moment. We apply this theorem to prove that the directed first and last 
passage
percolation problems in thin rectangles exhibit universal fluctuations 
given by
the Tracy-Widom law. In addition, we conjecture a precise value for the 
time
constant in the general first and last passage problems.


http://front.math.ucdavis.edu/math.PR/0412369

---------------------------------------------------------------

3004. LONGEST COMMON SUBSEQUENCES AND THE BERNOULLI MATCHING MODEL: 
NUMERICAL  WORK AND ANALYSES OF THE R-REACH SIMPLIFICATION

Jonah Blasiak

The expected length of longest common subsequences is a problem that 
has been
in the literature for at least twenty five years. Determining the 
limiting
constants \gamma_k appears to be quite difficult, and the current best 
bounds
leave much room for improvement. Boutet de Monvel explores an 
independent
version of the problem he calls the Bernoulli Matching model. He 
explores this
problem and its relation to the longest common subsequence problem. 
This paper
continues this pursuit by focusing on a simplification we term r-reach. 
For the
string model, L_r(u,v) is the longest common subsequence of u and v 
given that
each matched pair of letters is no more than r letters apart.


http://front.math.ucdavis.edu/math.PR/0412375

---------------------------------------------------------------

3005. NOISE STABILITY OF WEIGHTED MAJORITY

Yuval Peres

Benjamini, Kalai and Schramm (2001) showed that weighted majority 
functions
of $n$ independent unbiased bits are uniformly stable under noise: when 
each
bit is flipped with probability $\epsilon$, the probability 
$p_\epsilon$ that
the weighted majority changes is at most $C\epsilon^{1/4}$. They asked 
what is
the best possible exponent that could replace 1/4. We prove that the 
answer is
1/2. The upper bound obtained for $p_\epsilon$ is within a factor of
$\sqrt{\pi/2}+o(1)$ from the known lower bound when $\epsilon \to 0$ and
$n\epsilon\to \infty$.


http://front.math.ucdavis.edu/math.PR/0412377

---------------------------------------------------------------

3006. THE ESCAPE MODEL ON A HOMOGENEOUS TREE

G. Kordzakhia

There are two types of particles interacting on a homogeneous tree of 
degree
d + 1. The particles of the first type colonize the empty space with
exponential rate 1, but cannot take over the vertices that are occupied 
by the
second type. The particles of the second type spread with exponential 
rate
\lambda. They colonize the neighboring vertices that are either vacant 
or
occupied by the representatives of the opposite type, and annihilate the
particles of the type 1 as they reach them. There exists a critical 
value
\lambda_c =(2d - 1) + \sqrt{(2d -1)^2 -1} such that the first type 
survives
with positive probability for \lambda < \lambda_c, and dies out with
probability one for \lambda > \lambda_c.
  We also find the growth profile which characterizes the rate of growth 
of the
type 1 in the space-time on the event of survival.


http://front.math.ucdavis.edu/math.PR/0412392

---------------------------------------------------------------

3007. EXCITED RANDOM WALK IN ONE DIMENSION

T. Antal (1 and 2) and S. Redner (2 and 1) ((1) Boston University and  
(2) CNLS and   Los Alamos National Laboratory)

We study the excited random walk, in which a walk that is at a site that
contains cookies eats one cookie and then hops to the right with 
probability p
and to the left with probability q=1-p. If the walk hops onto an empty 
site,
there is no bias. For the 1-excited walk on the half-line (one cookie 
initially
at each site), the probability of first returning to the starting point 
at time
t scales as t^{-(2-p)}. Although the average return time to the origin 
is
infinite for all p, the walk eats, on average, only a finite number of 
cookies
until this first return when p<1/2. For the infinite line, the 
probability
distribution for the 1-excited walk has an unusual anomaly at the 
origin. The
positions of the leftmost and rightmost uneaten cookies can be 
accurately
estimated by probabilistic arguments and their corresponding 
distributions have
power-law singularities near the origin. The 2-excited walk on the 
infinite
line exhibits peculiar features in the regime p>3/4, where the walk is
transient, including a mean displacement that grows as t^{nu}, with 
nu>1/2
dependent on p, and a breakdown of scaling for the probability 
distribution of
the walk.


http://front.math.ucdavis.edu/math.PR/0412407

---------------------------------------------------------------

3008. ON THE INVARIANT MEASURE OF A POSITIVE RECURRENT DIFFUSION IN R

Michele L. Baldini

Given an one-dimensional positive recurrent diffusion governed by the
Stratonovich SDE \[ X_t=x+\int_0^t\sigma(X_s)\strat db(s)+\int_0^t 
m(X_s) ds,
\] we show that the associated stochastic flow of diffeomorphisms 
focuses as
fast as $ \mathrm{exp}(-2t\int_{R}\frac{m^2}{\sigma^2} d\Pi)$, where 
$d\Pi$ is
the finite stationary measure. Moreover, if the drift is reversed and 
the
diffeomorphism is inverted, then the path function so produced tends,
independently of its starting point, to a single (random) point whose
distribution is $d\Pi$. Applications to stationary solutions of $X_t$,
asymptotic behavior of solutions of SPDEs and random attractors are 
offered.


http://front.math.ucdavis.edu/math.PR/0412410

---------------------------------------------------------------

3009. NULL FLOWS, POSITIVE FLOWS AND THE STRUCTURE OF STATIONARY 
SYMMETRIC  STABLE PROCESSES

Gennady Samorodnitsky

This paper elucidates the connection between stationary symmetric
alpha-stable processes with 0<alpha<2 and nonsingular flows on measure 
spaces
by describing a new and unique decomposition of stationary stable 
processes
into those corresponding to positive flows and those corresponding to 
null
flows. We show that a necessary and sufficient for a stationary stable 
process
to be ergodic is that its positive component vanishes.


http://front.math.ucdavis.edu/math.PR/0412419

---------------------------------------------------------------

3010. MAXIMA OF ASYMPTOTICALLY GAUSSIAN RANDOM FIELDS AND MODERATE 
DEVIATION  APPROXIMATIONS TO BOUNDARY-CROSSING PROBABILITIES OF SUMS OF 
RANDOM VARIABLES
   WITH MULTIDIMENSIONAL INDICES

Hock Peng Chan and  Tze Leung Lai

Several classical results on boundary-crossing probabilities of Brownian
motion and random walks are extended to asymptotically Gaussian random 
fields,
which include sums of i.i.d. random variables with multidimensional 
indices,
multivariate empirical processes, and scan statistics in change-point 
and
signal detection as special cases. Some key ingredients in these 
extensions are
moderate deviation approximations to marginal tail probabilities and 
weak
convergence of the conditional distributions of certain ``clumps'' 
around
high-level crossings. We also discuss how these results are related to 
the
Poisson clumping heuristic and tube formulas of Gaussian random fields, 
and
describe their applications to laws of the iterated logarithm in the 
form of
the Kolmogorov--Erdos--Feller integral tests.


http://front.math.ucdavis.edu/math.PR/0412428

---------------------------------------------------------------

3011. A QUANTUM VERSION OF SANOV'S THEOREM

I. Bjelakovic and  J.-D. Deuschel and  T. Krueger and  R. Seiler and  
Ra.  Siegmund-Schultze, A. Szkola

We present a quantum extension of a version of Sanov's theorem 
focussing on a
hypothesis testing aspect of the theorem: There exists a sequence of 
typical
subspaces for a given set $\Psi$ of stationary quantum product states
asymptotically separating them from another fixed stationary product 
state.
Analogously to the classical case, the exponential separating rate is 
equal to
the infimum of the quantum relative entropy with respect to the quantum
reference state over the set $\Psi$. However, while in the classical 
case the
separating subsets can be chosen universal, in the sense that they 
depend only
on the chosen set of i.i.d. processes, in the quantum case the choice 
of the
separating subspaces depends additionally on the reference state.


http://front.math.ucdavis.edu/quant-ph/0412157

---------------------------------------------------------------

3012. RELAXATION TIME OF L-REVERSAL CHAINS AND OTHER CHROMOSOME SHUFFLES

Nicoletta Cancrini and  Pietro Caputo and Fabio Martinelli

We prove tight bounds on the relaxation time of the so called 
$L$--reversal
chain, introduced by R. Durrett as a stochastic model for the evolution 
of
chromosome chains. The process is described as follows: we have $n$ 
distinct
letters on the vertices of the $n$--cycle ($\bbZ$ mod $n$); at each 
step a
connected subset of the graph is chosen uniformly at random among all 
those of
length at most $L$ and the current permutation is shuffled by reversing 
the
order of the letters over that subset. We show that the relaxation time
$\t(n,L)$, defined as the inverse of the spectral gap of the associated 
Markov
generator, satisfies $\t(n,L)=O(n \vee \frac{n^3}{L^3})$. Our results 
can be
interpreted as a strong evidence for a conjecture of R. Durrett of a 
similar
behavior for the mixing time of the chain.


http://front.math.ucdavis.edu/math.PR/0412449

---------------------------------------------------------------

3013. ON RANDOM $\PM 1$ MATRICES: SINGULARITY AND DETERMINANT

Terence Tao and  Van Vu

We consider several questions concerning the determinant of a random 
$\pm 1$
matrix, in particular computing the probability on when this 
determinant is
zero or close to zero. We present simpler proofs of existing results and
introduce some new ones.


http://front.math.ucdavis.edu/math.CO/0411095

---------------------------------------------------------------

3014. PHASE ORDERING AFTER A DEEP QUENCH: THE STOCHASTIC ISING AND HARD 
CORE  GAS MODELS ON A TREE

Pietro Caputo and Fabio Martinelli

Consider a low temperature stochastic Ising model in the phase 
coexistence
regime with Markov semigroup $P_t$. A fundamental and still largely open
problem is the understanding of the long time behavior of $\d_\h P_t$ 
when the
initial configuration $\h$ is sampled from a highly disordered state 
$\nu$
(e.g. a product Bernoulli measure or a high temperature Gibbs measure).
Exploiting recent progresses in the analysis of the mixing time of 
Monte Carlo
Markov chains for discrete spin models on a regular $b$-ary tree 
$\Tree^b$, we
tackle the above problem for the Ising and hard core gas (independent 
sets)
models on $\Tree^b$. If $\nu$ is a biased product Bernoulli law then, 
under
various assumptions on the bias and on the thermodynamic parameters, we 
prove
$\nu$-almost sure weak convergence of $\d_\h P_t$ to an extremal Gibbs 
measure
(pure phase) and show that the limit is approached at least as fast as a
stretched exponential of the time $t$. In the context of randomized 
algorithms
and if one considers the Glauber dynamics on a large, finite tree, our 
results
prove fast local relaxation to equilibrium on time scales much smaller 
than the
true mixing time, provided that the starting point of the chain is not 
taken as
the worst one but it is rather sampled from a suitable distribution.


http://front.math.ucdavis.edu/math.PR/0412450

---------------------------------------------------------------

3015. A QUESTION ABOUT PARISI FUNCTIONAL

Dmitry Panchenko

We conjecture that the Parisi functional in the SK model is convex in 
the
functional order parameter and prove a partial result that shows the 
convexity
along one-sided directions. A consequence of this result is 
log-convexity of
L_1 norm for a class or random variables.


http://front.math.ucdavis.edu/math.PR/0412463

---------------------------------------------------------------

3016. SELF-ORGANIZED FOREST-FIRES NEAR THE CRITICAL TIME

J. van den Berg and  R. Brouwer

We consider a forest-fire model which, somewhat informally, is 
described as
follows: Each site (vertex) of the square lattice is either vacant or 
occupied
by a tree.Vacant sites become occupied at rate 1. Further, each site is 
hit by
lightningat rate lambda. This lightning instantaneously destroys (makes 
vacant)
the occupied cluster of the site. This model is closely related to the
Drossel-Schwabl forest-fire model, which has received much attention in 
the
physics literature. The most interesting behaviour seems to occur when 
the
lightning rate goes to zero. In the physics literature it is believed 
that then
the system has so-called self-organized critical behaviour.
   We let the system start with all sites vacant and study, for positive 
but
small lambda,the behaviour near the `critical time' tc; that is, the 
time after
which in the modified system without lightning an infinite occupied 
cluster
would emerge.
   Intuitively one might expect that if, for fixed t > tc, we let 
simultaneously
lambda tend to 0 and m to infinity, the probability that some tree at 
distance
smaller than m from O is burnt before time t goes to 1. However, we 
show that
under a percolation-like assumption (which we can not prove but believe 
to be
true) this intuition is false. We compare with the case where the square
lattice is replaced by the directed binary tree, and pose some natural 
open
problems.


http://front.math.ucdavis.edu/math.PR/0412488

---------------------------------------------------------------

3017. EXCHANGEABLE GIBBS PARTITIONS AND STIRLING TRIANGLES

Alexander Gnedin and Jim Pitman

For two collections of nonnegative and suitably normalised weights
$\W=(\W_j)$ and $\V=(\V_{n,k})$, a probability distribution on the set 
of
partitions of the set $\{1,...,n\}$ is defined by assigning to a generic
partition $\{A_j, j\leq k\}$ the probability $\V_{n,k} \W_{|A_1|}...
\W_{|A_k|}$, where $|A_j|$ is the number of elements of $A_j$. We impose
constraints on the weights by assuming that the resulting random 
partitions
$\Pi_n$ of $[n]$ are consistent as $n$ varies, meaning that they define 
an
exchangeable partition of the set of all natural numbers. This implies 
that the
weights $\W$ must be of a very special form depending on a single 
parameter
$\alpha\in [-\infty,1]$. The case $\alpha=1$ is trivial, and for each 
value of
$\alpha\neq 1$ the set of possible $\V$-weights is an 
infinite-dimensional
simplex. We identify the extreme points of the simplex by solving the 
boundary
problem for a generalised Stirling triangle. In particular, we show 
that the
boundary is discrete for $-\infty\leq\alpha<0$ and continuous for
$0\leq\alpha<1$. For $\alpha\leq 0$ the extremes correspond to the 
members of
the Ewens-Pitman family of random partitions indexed by 
$(\alpha,\theta)$,
while for $0<\alpha<1$ the extremes are obtained by conditioning an
$(\alpha,\theta)$-partition on the asymptotics of the number of blocks 
of
$\Pi_n$ as $n$ tends to infinity.


http://front.math.ucdavis.edu/math.PR/0412494

---------------------------------------------------------------

3018. FUNCTION-VALUED STOCHASTIC CONVOLUTIONS ARISING IN 
INTEGRODIFFERENTIAL  EQUATIONS

Anna Karczewska

We study stochastic convolutions providing by fundamental solutions of a
class of integrodifferential equations which interpolate the heat and 
the wave
equations. We give sufficient condition for the existence of 
function--valued
convolutions in terms of the covariance kernel of a noise given by 
spatially
homogeneous Wiener process.


http://front.math.ucdavis.edu/math.PR/0412495

---------------------------------------------------------------

3019. MAXIMAL TYPE INEQUALITIES FOR LINEAR STOCHASTIC VOLTERRA EQUATIONS

Anna Karczewska

The paper is devoted to estimates for convolutions appearing in some 
class of
stochastic Volterra equations. Two maximal inequalities and exponential 
tail
estimate are provided. In the paper the fractional method of infinite
dimensional stochastic calculus has been used.


http://front.math.ucdavis.edu/math.PR/0412496

---------------------------------------------------------------

3020. SHARP THRESHOLDS AND PERCOLATION IN THE PLANE

Bela Bollobas and Oliver Riordan

Recently, the authors showed that the critical probability for random 
Voronoi
percolation in the plane is 1/2. A by-product of the method was a short 
proof
of the Harris-Kesten Theorem concerning bond percolation in the planar 
square
lattice. The aim of this paper is to show that the same techniques can 
be
applied to many other planar percolation models, both to obtain short 
proofs of
known results, and to prove new ones.


http://front.math.ucdavis.edu/math.PR/0412510

---------------------------------------------------------------

3021. STOCHASTIC VOLTERRA CONVOLUTION WITH L\'EVY PROCESS

Anna Karczewska

In the paper we study stochastic convolution appearing in Volterra 
equation
driven by so called L\'evy process. By L\'evy process we mean a process 
with
homogeneous independent increments, continuous in probability and 
cadlag.


http://front.math.ucdavis.edu/math.PR/0411148

---------------------------------------------------------------

3022. WHY DELANNOY NUMBERS?

Cyril Banderier (LIPN) and  Sylviane Schwer (LIPN)

This article is not a research paper, but a little note on the history 
of
combinatorics: We present here a tentative short biography of Henri 
Delannoy,
and a survey of his most notable works. This answers to the question 
raised in
the title, as these works are related to lattice paths enumeration, to 
the
so-called Delannoy numbers, and were the first general way to solve 
Ballot-like
problems. These numbers appear in probabilistic game theory, alignments 
of DNA
sequences, tiling problems, temporal representation models, analysis of
algorithms and combinatorial structures.


http://front.math.ucdavis.edu/math.CO/0411128

---------------------------------------------------------------

3023. GENERATING FUNCTIONS FOR KERNELS OF DIGRAPHS (ENUMERATION & 
ASYMPTOTICS  FOR NIM GAMES)

Cyril Banderier (LIPN) and  Jean-Marie Le Bars (LIPN and  GREYC) and  
Vlady  Ravelomanana (LIPN)

In this article, we study directed graphs (digraphs) with a coloring
constraint due to Von Neumann and related to Nim-type games. This is 
equivalent
to the notion of kernels of digraphs, which appears in numerous fields 
of
research such as game theory, complexity theory, artificial intelligence
(default logic, argumentation in multi-agent systems), 0-1 laws in 
monadic
second order logic, combinatorics (perfect graphs)... Kernels of 
digraphs lead
to numerous difficult questions (in the sense of NP-completeness,
#P-completeness). However, we show here that it is possible to use a 
generating
function approach to get new informations: we use technique of symbolic 
and
analytic combinatorics (generating functions and their singularities) 
in order
to get exact and asymptotic results, e.g. for the existence of a kernel 
in a
circuit or in a unicircuit digraph. This is a first step toward a
generatingfunctionology treatment of kernels, while using, e.g., an 
approach "a
la Wright". Our method could be applied to more general "local coloring
constraints" in decomposable combinatorial structures.


http://front.math.ucdavis.edu/math.CO/0411138

---------------------------------------------------------------

3024. INFINITE DIMENSIONAL ENTANGLED MARKOV CHAINS

Francesco Fidaleo

We continue the analysis of nontrivial examples of quantum Markov 
processes.
This is done by applying the construction of entangled Markov chains 
obtained
from classical Markov chains with infinite state--space. The formula 
giving the
joint correlations arises from the corresponding classical formula by 
replacing
the usual matrix multiplication by the Schur multiplication. In this 
way, we
provide nontrivial examples of entangled Markov chains on 
$\bar{\cup_{J\subset
Z} \bar{\otimes}_{J}F}^{C^{*}}$, $F$ being any infinite dimensional 
type $I$
factor, $J$ a finite interval of $Z$, and the bar the von Neumann tensor
product between von Neumann algebras. We then have new nontrivial 
examples of
quantum random walks which could play a r\^ole in quantum information 
theory.
   In view of applications to quantum statistical mechanics too, we see 
that the
ergodic type of an entangled Markov chain is completely determined by 
the
corresponding ergodic type of the underlying classical chain, provided 
that the
latter admits an invariant probability distribution. This result 
parallels the
corresponding one relative to the finite dimensional case.
   Finally, starting from random walks on discrete ICC groups, we exhibit
examples of quantum Markov processes based on type $II_1$ von Neumann 
factors.


http://front.math.ucdavis.edu/math.OA/0411202

---------------------------------------------------------------

3025. ON THE SPECTRUM OF MARKOV SEMIGROUPS VIA SAMPLE PATH LARGE 
DEVIATIONS

Irina Ignatiouk-Robert

The essential spectral radius of a sub-Markovian process is defined as 
the
infimum of the spectral radiuses of all local perturbations of the 
process.
When the family of rescaled processes satisfies sample path large 
deviation
principle, the spectral radius and the essential spectral radius are 
expressed
in terms of the rate function. The paper is motivated by applications to
reflected diffusions and jump Markov processes describing stochastic 
networks
for which the sample path large deviation principle has been 
established and
the rate function has been identified while essential spectral radius 
has not
been calculated.


http://front.math.ucdavis.edu/math.PR/0411221

---------------------------------------------------------------

3026. DIRECTED POLYMERS IN RANDOM ENVIRONMENT ARE DIFFUSIVE AT WEAK 
DISORDER

Francis Comets (PMA) and  Nobuo Yoshida (DIVISION of Mathematics and  
Kyoto  University)

In this paper, we consider directed polymers in random environment with
discrete space and time. For transverse dimension at least equal to 3, 
we prove
that diffusivity holds for the path in the full weak disorder region, 
i.e.,
where the partition function differs from its annealed value only by a
non-vanishing factor. Deep inside this region, we also show that the 
quenched
averaged energy has fluctuations of order 1. In complete generality 
(arbitrary
dimension and temperature), we prove monotonicity of the phase diagram 
in the
temperature.


http://front.math.ucdavis.edu/math.PR/0411223

---------------------------------------------------------------

3027. POISSON CALCULUS FOR SPATIAL NEUTRAL TO THE RIGHT PROCESSES

Lancelot F. James

In this paper we consider classes of nonparametric priors on spaces of
distribution functions and cumulative hazards that are based on 
extensions of
the neutral to the right concept. In particular we extend the 
definition of NTR
processes from the real line to classes of distributions on general 
spaces.
Representations of the posterior distributions are given using a 
different type
of calculus than traditionally used in the Bayesian literature. The 
techniques
are applied to progressively more complex models. Refinements are then 
given
which describes the underlying properties of spatial NTR models 
analogous to
those developed for the Dirihclet process. The analysis yields 
accessible
moment formulae and characterizations of the the posterior distribution 
and
relavant marginal distributions. In the homogeneous case this work 
turns out to
be connected to and overlap with recent work on regenerative 
compositions
defined by a suitable discretisation of subordinators. The results also 
have
connections to other related work on exponential functionals of 
subordinators.
In addition, we develop results for spatial NTR mixture models and 
identify a
class of species sampling models derived from spatial NTR processes.


http://front.math.ucdavis.edu/math.ST/0305053

---------------------------------------------------------------

3028. ON A MULTIVARIATE VERSION OF BERNSTEIN'S INEQUALITY

P. Major

We prove a multivariate version of Bernstein's inequality about the
probability that degenerate $U$-statistics take a value larger than 
some number
$u$. This is an improvement of former estimates for the same problem 
which
yields an asymptotically sharp estimate for not too large numbers $u$. 
This
paper also contains an analogous bound about the distribution of 
multiple
Wiener-Ito integrals. Their comparison shows that our results are 
sharp. The
proofs are based on good estimates about high moments of multiple random
integrals. They are obtained by means of a diagram formula which 
enables us to
express the product of multiple random integrals as the sum of such
expressions.


http://front.math.ucdavis.edu/math.PR/0411287

---------------------------------------------------------------

3029. A MULTIVARIATE GENERALIZATION OF HOEFFDING'S INEQUALITY

P. Major

We prove a multivariate version of Hoeffding's inequality about the
distribution of homogeneous polynomials of Rademacher functions. The 
proof is
based on such an estimate about the moments of homogeneous polynomials 
of
Rademacher functions which can be considered as an improvement of 
Borell's
inequality in a most important special case.


http://front.math.ucdavis.edu/math.PR/0411288

---------------------------------------------------------------

3030. ALPHA-PFAFFIAN, PFAFFIAN POINT PROCESS AND SHIFTED SCHUR MEASURE

Sho Matsumoto

For any complex number $\alpha$ and any even-size skew-symmetric matrix 
$B$,
we define a generalization $\pfa{\alpha}(B)$ of the pfaffian $\pf(B)$ 
which we
call the $\alpha$-pfaffian. The $\alpha$-pfaffian is a pfaffian 
analogue of the
$\alpha$-determinant. It gives the pfaffian at $\alpha=-1$. We give some
formulas for $\alpha$-pfaffians and study the positivity. Further we 
define
point processes determined by the $\alpha$-pfaffian. Also we provide a 
linear
algebraic proof of the explicit pfaffian expression for the correlation
function of the shifted Schur measure.


http://front.math.ucdavis.edu/math.CO/0411277

---------------------------------------------------------------

3031. GUNDY'S DECOMPOSITION FOR NON-COMMUTATIVE MARTINGALES AND 
APPLICATIONS

Javier Parcet and Narcisse Randrianantoanina

We provide an analogue of Gundy's decomposition for L1-bounded
non-commutative martingales. An important difference from the classical 
case is
that for any L1-bounded non-commutative martingale, the decomposition 
consists
of four martingales. This is strongly related with the row/column 
nature of
non-commutative Hardy spaces of martingales. As applications, we obtain 
simpler
proofs of the weak type (1,1) boundedness for non-commutative martingale
transforms and the non-commutative analogue of Burkholder's weak type
inequality for square functions. A sequence (x_n) in a normed space X 
is called
2-co-lacunary if there exists a bounded linear map from the closed 
linear span
of (x_n) to l2 taking each x_n to the n-th vector basis of l2. We prove 
(using
our decomposition) that any relatively weakly compact martingale 
difference
sequence in L1(M,\tau) whose sequence of norms is bounded away from 
zero is
2-co-lacunary, generalizing a result of Aldous and Fremlin to 
non-commutative
L1-spaces.


http://front.math.ucdavis.edu/math.OA/0411296

---------------------------------------------------------------

3032. ON THE RECONSTRUCTION OF THE DRIFT OF A DIFFUSION FROM TRANSITION 
  PROBABILITIES WHICH ARE PARTIALLY OBSERVED IN SPACE

Sergio Albeverio and Carlo Marinelli

The problem of reconstructing the drift of a diffusion in $\erre^d$, 
$d\geq
2$, from the transition probability density observed outside a domain is
considered. The solution of this problem also solves a new inverse 
problem for
a class of parabolic partial differential equations. This work 
considerably
extends \cite{jsp} in terms of generality, both concerning assumptions 
on the
drift coefficient, and allowing for non-constant diffusion coefficient.
Sufficient conditions for solvability of this type of inverse problem 
for $d=1$
are also given.


http://front.math.ucdavis.edu/math.PR/0411008

---------------------------------------------------------------

3033. SOME REMARKS ON COMMUTATION RELATIONS FOR SLE

Julien Dubedat

Schramm-Loewner Evolutions (SLEs) describe a one-parameter family of 
growth
processes in the plane that have particular conformal invariance 
properties.
For instance, SLE can define simple random curves in a simply conneccted
domain. In this paper we are interested in questions pertaining to the
definition of several SLEs in a domain (i.e. several random curves). In
particular, one derives infinitesimal commutation conditions, discuss 
some
solutions, and show how to lift these infinitesimal relations to global
relations in simple cases.


http://front.math.ucdavis.edu/math.PR/0411299

---------------------------------------------------------------

3034. ALMOST GLOBAL STOCHASTIC STABILITY

Ramon van Handel

We develop a method to prove almost global stability of stochastic
differential equations in the sense that almost every initial point 
(with
respect to the Lebesgue measure) is asymptotically attracted to the 
origin with
unit probability. The method can be viewed as a dual to Lyapunov's 
second
method for stochastic differential equations and extends the 
deterministic
result in [A. Rantzer, Syst. Contr. Lett., 42 (2001), pp. 161--168]. 
The result
can also be used in certain cases to find stabilizing controllers for
stochastic nonlinear systems using convex optimization. The main 
technical tool
is the theory of stochastic flows of diffeomorphisms.


http://front.math.ucdavis.edu/math.PR/0411311

---------------------------------------------------------------

3035. THE EMPIRICAL DISTRIBUTION OF THE EIGENVALUES OF A GRAM MATRIX 
WITH A  GIVEN VARIANCE PROFILE

W. Hachem and P. Loubaton and J. Najim

Consider a $N\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the 
entries are
given by $Y_{ij}^{n}=\frac{\sigma(i/N,j/n)}{\sqrt{n}} X_{ij}^{n}$, the
$X_{ij}^{n}$ being centered i.i.d. and $\sigma:[0,1]^2 \to (0,\infty)$ 
being a
continuous function called a variance profile. Consider now a 
deterministic
$N\times n$ matrix $\Lambda_n=(\Lambda_{ij}^{n})$ whose non diagonal 
elements
are zero. Denote by $\Sigma_n$ the non-centered matrix $Y_n + 
\Lambda_n$. Then
under the assumption that $\lim_{n\to \infty} \frac Nn =c>0$ and $$ 
\frac{1}{N}
\sum_{i=1}^{N} \delta_{(\frac{i}{N}, (\Lambda_{ii}^n)^2)} 
\xrightarrow[n\to
\infty]{} H(dx,d\lambda), $$ where $H$ is a probability measure, it is 
proven
that the empirical distribution of the eigenvalues of $ \Sigma_n 
\Sigma_n^T$
converges almost surely in distribution to a non random probability 
measure.
This measure is characterized in terms of its Stieltjes transform, 
which is
obtained with the help of an auxiliary system of equations. This kind of
results is of interest in the field of wireless communication.


http://front.math.ucdavis.edu/math.PR/0411333

---------------------------------------------------------------

3036. DEVIATIONS OF A RANDOM WALK IN A RANDOM SCENERY WITH STRETCHED  
EXPONENTIAL TAILS

Remco van der Hofstad and  Nina Gantert and Wolfgang K{\"o}nig

Let $(Z_n)_{n\in\N_0}$ be a d-dimensional random walk in random scenery,
i.e., $Z_n=\sum_{k=0}^{n-1}Y_{S_k}$ with $(S_k)_{k\in\N_0}$ a random 
walk in
$\Z^d$ and $(Y_{z})_{z\in\Z^d}$ an i.i.d. scenery, independent of the 
walk.
   We assume that the random variables $Y_{z}$ have a stretched 
exponential
tail. In particular, they do not possess exponential moments. We 
identify the
speed and the rate of the logarithmic decay of $\P(\frac 1n Z_n>t_n)$ 
for all
sequences $(t_n)_{n\in\N}$ satisfying a certain lower bound. This 
complements
results of \cite{GKS04}, where it was assumed that $Y_{z}$ has 
exponential
moments of all orders. Informally, in contrast to the situation 
\cite{GKS04},
the event $\{\frac 1n Z_n>t_n\}$ is not realized by a homogeneous 
behavior of
the walk's local times and the scenery, but by many visits of the 
walker to a
particular site and a large value of the scenery at that site. This 
reflects a
well-known extreme behavior typical for random variables having no 
exponential
moments.


http://front.math.ucdavis.edu/math.PR/0411361

---------------------------------------------------------------

3037. AN EXTREME-VALUE ANALYSIS OF THE LIL FOR BROWNIAN MOTION

Davar Khoshnevisan and  David A. Levin and  Zhan Shi

We present an extreme-value analysis of the classical law of the 
iterated
logarithm (LIL) for Brownian motion. Our result can be viewed as a new
improvement to the LIL.


http://front.math.ucdavis.edu/math.PR/0411376

---------------------------------------------------------------

3038. THE HYPERBOLIC GEOMETRY OF RANDOM TRANSPOSITIONS

Nathanael Berestycki

Make the set of permutations of $n$ objects into a graph $G_n$ by 
connecting
two permutations that differ by one transposition, and let $\sigma_t$ 
be the
continuous time simple random walk on this graph. In a previous paper,
Berestycki and Durrett (2004) showed that the limiting behavior of the 
distance
from the identity at time $cn/2$ has a phase transition at $c=1$. When 
$c<1$,
it is asymptotically $cn/2$, while for $c>1$ it is $u(c)n$ with $u(c) < 
c/2$.
Here we investigate some consequences of this result for the geometry 
of $G_n$.
Our first result is that when we consider the sphere of radius $an$ 
centered at
the origin, and pick two points independently according to the hitting
distribution, then Gromov hyperbolicity breaks down at critical radius 
$a=1/4$.
When $a<1/4$ the space is hyperbolic but also displays behavior that is 
much
different from manifolds of negative curvature - it is shown that there 
are
many geodesics that may travel much different paths to get to a point. 
We also
show that the hitting distribution of the sphere of radius $an$ is
asymptotically singular with respect to the uniform distribution. 
Finally, we
prove that the qualitative behavior of the Gromov hyperbolicity 
persists if we
pick points independently according to the uniform measure on the 
sphere of
radius $an$. However, in this case, the critical radius is $a=1-\log 2$.


http://front.math.ucdavis.edu/math.PR/0411011

---------------------------------------------------------------

3039. LARGE DEVIATIONS FOR DIFFUSIONS WITH TIME PERIODIC DRIFT AND 
STOCHASTIC  RESONANCE

Samuel Herrmann and  Peter Imkeller and  Dierk Peithmann

We consider potential type dynamical systems in finite dimensions with 
two
meta-stable states. They are subject to two sources of perturbation: a 
slow
external periodic perturbation of period $T$ and a small Gaussian random
perturbation of intensity $\eps$, and therefore mathematically 
described as
weakly time inhomogeneous diffusion processes. A system is in stochastic
resonance provided the small noisy perturbation is tuned in such a way 
that its
random trajectories follow the exterior periodic motion in an optimal 
fashion,
i.e. for some optimal intensity $\eps(T)$. The physicists' favorite 
measures of
quality of periodic tuning -- and thus stochastic resonance -- such as 
spectral
power amplification or signal-to-noise ratio have proven to be 
defective. They
are not robust w.r.t. effective model reduction, i.e. for the passage 
to a
simplified finite state Markov chain model reducing the dynamics to a 
pure
jumping between the meta-stable states of the original system. An 
entirely
probabilistic notion of stochastic resonance based on the transition 
dynamics
between the domains of attraction of the meta-stable states -- and thus 
failing
to suffer from this robustness defect -- was proposed before in the 
context of
one-dimensional diffusions. It is investigated for higher dimensional 
systems
here, by using extensions and refinements of the Freidlin-Wentzell 
theory of
large deviations for time homogeneous diffusions. Large deviation 
principles
developed for weakly time inhomogeneous diffusions prove to be key 
tools for a
treatment of the problem of diffusion exit from a domain and thus for 
the
approach of stochastic resonance via transition probabilities between
meta-stable sets.


http://front.math.ucdavis.edu/math.PR/0411386

---------------------------------------------------------------

3040. COSINE PRODUCTS, FOURIER TRANSFORMS, AND RANDOM SUMS

Kent E. Morrison

We investigate several infinite product of cosines and find the closed 
form
using the Fourier transform. The answers provide limiting distributions 
for
some elementary probability experiments.


http://front.math.ucdavis.edu/math.CA/0411380

---------------------------------------------------------------

3041. POLYNUCLEAR GROWTH MODEL, GOE$^2$ AND RANDOM MATRIX WITH 
DETERMINISTIC  SOURCE

T. Imamura and T. Sasamoto

We present a random matrix interpretation of the distribution functions 
which
have appeared in the study of the one-dimensional polynuclear growth 
(PNG)
model with external sources. It is shown that the distribution, 
GOE$^2$, which
is defined as the square of the GOE Tracy-Widom distribution, can be 
obtained
as the scaled largest eigenvalue distribution of a special case of a 
random
matrix model with a deterministic source, which have been studied in a
different context previously. Compared to the original interpretation 
of the
GOE$^2$ as ``the square of GOE'', ours has an advantage that it can also
describe the transition from the GUE Tracy-Widom distribution to the 
GOE$^2$.
   We further demonstrate that our random matrix interpretation can be 
obtained
naturally by noting the similarity of the topology between a certain
non-colliding Brownian motion model and the multi-layer PNG model with 
an
external source. This provides us with a multi-matrix model 
interpretation of
the multi-point height distributions of the PNG model with an external 
source.


http://front.math.ucdavis.edu/math-ph/0411057

---------------------------------------------------------------

3042. DOBRUSHIN-KOTECKY-SCHLOSMAN THEOREM FOR POLYGONAL MARKOV FIELDS 
IN THE  PLANE

Tomasz Schreiber

We establish a version of the Dobrushin-Kotecky-Schlosman phase 
separation
theorem for the length-interacting Arak-Surgailis polygonal Markov 
fields with
V-shaped nodes.


http://front.math.ucdavis.edu/math-ph/0411064

---------------------------------------------------------------

3043. DISTRIBUTION FUNCTIONS FOR EDGE EIGENVALUES IN ORTHOGONAL AND 
SYMPLECTIC

Momar Dieng

We derive Painlev\'e--type expressions for the distribution of the 
$m^{th}$
largest eigenvalue in the Gaussian Orthogonal and Symplectic Ensembles 
in the
edge scaling limit. The work of Johnstone and Soshnikov (see [7], [10]) 
implies
the immediate relevance of our formulas for the $m^{th}$ largest 
eigenvalue of
the appropriate Wishart distribution.


http://front.math.ucdavis.edu/math.PR/0411421

---------------------------------------------------------------

3044. QUANTUM HELE-SHAW FLOW

Haakan Hedenmalm and Nikolai Makarov

In this note, we discuss the quantum Hele-Shaw flow, a random measure 
process
in the complex plane introduced by the physicists P.Wiegmann, A. 
Zabrodin, et
al. This process arises in the theory of electronic droplets confined 
to a
plane under a strong magnetic field, as well as in the theory of random 
normal
matrices. We extend a result of Elbau and Felder to general external 
field
potentials, and also show that if the potential is $C^2$-smooth, then 
the
quantum Hele-Shaw flow converges, under appropriate scaling, to the 
classical
(weighted) Hele-Shaw flow, which can be modeled in terms of an obstacle
problem.


http://front.math.ucdavis.edu/math.PR/0411437

---------------------------------------------------------------

3045. FISHER'S INFORMATION FOR DISCRETELY SAMPLED LEVY PROCESSES

Yacine Ait-Sahalia and  Jean Jacod (PMA)

This paper studies the asymptotic behavior of the Fisher information 
for a
Levy process discretely sampled at an increasing frequency. We show 
that it is
possible to distinguish not only the continuous part of the process 
from its
jumps part, but also different types of jumps, and derive the rates of
convergence of efficient estimators.


http://front.math.ucdavis.edu/math.PR/0411438

---------------------------------------------------------------

3046. GREEDY LATTICE ANIMALS: GEOMETRY AND CRITICALITY (WITH AN 
APPENDIX)

Alan Hammond

Assign to each site of the integer lattice $\Zd$ a real score, sampled
according to the same distribution $F$, independently of the choices 
made at
all other sites. A lattice animal is a finite connected set of sites, 
with its
weight being the sum of the scores at its sites. Let $N_n$ be the 
maximal
weight of those lattice animals of size $n$ that contain the origin. 
Denote by
$N$ the almost sure finite constant limit of $n^{-1} N_n$, which exists 
under a
mild condition on the positive tail of $F$. We study certain geometrical
aspects of the lattice animal with maximal weight among those contained 
in an
$n$-box where $n$ is large, both in the supercritical phase where $N > 
0$, and
in the critical case where $N = 0$.


http://front.math.ucdavis.edu/math.PR/0411459

---------------------------------------------------------------

3047. THE LARGEST EIGENVALUE OF SMALL RANK PERTURBATIONS OF HERMITIAN 
RANDOM  MATRICES

Sandrine P\'ech\'e

We compute the limiting eigenvalue statistics at the edge of the 
spectrum of
large Hermitian random matrices perturbed by the addition of small rank
deterministic matrices. To be more precise, we consider random Hermitian
matrices with independent Gaussian entries $M_{ij}, i\leq j$ with 
various
expectations. We prove that the largest eigenvalue of such random 
matrices
exhibits, in the large $N$ limit, various limiting distributions 
depending on
both the eigenvalues of the matrix $(\mathbb{E}M_{ij})_{i,j=1}^N$ and 
its rank.


http://front.math.ucdavis.edu/math.PR/0411487

---------------------------------------------------------------

3048. STATISTICALLY DUAL DISTRIBUTIONS AND ESTIMATION OF THE PARAMETERS

S.I. Bityukov and  V.V. Smirnova and  V.A. Taperechkina

The reconstruction of the parameter of the model by the measurement of 
the
random variable depending on this parameter is one of the main tasks of
statistics. In the paper the notion of the statistically dual 
distributions is
introduced. The approach, based on the properties of the statistically 
dual
distributions, to resolving of the given task is proposed.


http://front.math.ucdavis.edu/math.ST/0411462

---------------------------------------------------------------

3049. SPONTANEOUS DYNAMICS OF ASYMMETRIC RANDOM RECURRENT SPIKING 
NEURAL  NETWORKS

H. Soula and  G. Beslon and  O. Mazet

We study in this paper the effect of an unique initial stimulation on 
random
recurrent networks of leaky integrate and fire neurons. Indeed given a
stochastic connectivity this so-called spontaneous mode exhibits 
various non
trivial dynamics. This study brings forward a mathematical formalism 
that
allows us to examine the variability of the afterward dynamics 
according to the
parameters of the weight distribution. Provided independence hypothesis 
(e.g.
in the case of very large networks) we are able to compute the average 
number
of neurons that fire at a given time -- the spiking activity. In 
accordance
with numerical simulations, we prove that this spiking activity reaches 
a
steady-state, we characterize this steady-state and explore the 
transients.


http://front.math.ucdavis.edu/cs.NE/0411052

---------------------------------------------------------------

3050. FAST NON-PARAMETRIC BAYESIAN INFERENCE ON INFINITE TREES

Marcus Hutter

Given i.i.d. data from an unknown distribution, we consider the problem 
of
predicting future items. An adaptive way to estimate the probability 
density is
to recursively subdivide the domain to an appropriate data-dependent
granularity. A Bayesian would assign a data-independent prior 
probability to
"subdivide", which leads to a prior over infinite(ly many) trees. We 
derive an
exact, fast, and simple inference algorithm for such a prior, for the 
data
evidence, the predictive distribution, the effective model dimension, 
and other
quantities.


http://front.math.ucdavis.edu/math.ST/0411515

---------------------------------------------------------------

3051. EXCHANGEABLE PAIRS AND POISSON APPROXIMATION

Sourav Chatterjee and  Persi Diaconis and  Elizabeth Meckes

This is a survery paper on Poisson approximation using Stein's method of
exchangeable pairs. We illustrate using Poisson-binomial trials and many
variations on three classical problems of combinatorial probability: the
matching problem, the coupon collector's problem, and the birthday 
problem.
While many details are new, the results are closely related to a body 
of work
developed by Andrew Barbour, Louis Chen, Richard Arratia, Lou Gordon, 
Larry
Goldstein, and their collaborators. Some comparison with these other 
approaches
is offered.


http://front.math.ucdavis.edu/math.PR/0411525

---------------------------------------------------------------

3052. FLUCTUATION OF PLANAR BROWNIAN LOOP CAPTURING LARGE AREA

Alan Hammond and Yuval Peres

We consider a planar Brownian loop $B$ that is run for a time $T$ and
conditioned on the event that its range encloses the unusually high 
area of
$\pi T^2$, with $T$ being large. We study the deviation of the range of 
the
conditioned process $X$ from a circle of radius $T$, as a model for the
fluctuation of a phase boundary. This deviation is measured by means of 
the
inradius and outradius of the region enclosed by the range of $X$. We 
prove
that in a typical realization of the conditioned measure, each of these
quantities differs from $T$ by at most $T^{2/3 + \epsilon}$.


http://front.math.ucdavis.edu/math.PR/0411540

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3053. THE INITIAL DRIFT OF A 2D DROPLET AT ZERO TEMPERATURE

Raphael Cerf and  Sana Louhichi

We consider the 2D stochastic Ising model evolving according to the 
Glauber
dynamics at zero temperature. We compute the initial drift for droplets 
which
are discretizations of smooth domains. A specific spatial average of the
derivative at time~0 of the volume variation of a droplet close to a 
boundary
point is equal to its curvature multiplied by a direction dependent
coefficient. For a boundary point having a tangent with angle $\theta$, 
this
coefficient is equal to $-\frac{\textstyle 1}{\textstyle 2}|\cos 
2\theta|$.


http://front.math.ucdavis.edu/math.PR/0411545

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3054. THE EFFECT OF FINITE MEMORY CUTOFF ON LOOP ERASED WALK IN Z^3

Wei-Shih Yang and Aklilu Zeleke

Let \zeta be the intersection exponent of random walks in Z^3 and 
\alpha be a
positive real number. We construct a stochastic process from a simple 
random
walk by erasing loops of length at most N^\alpha. We will prove that 
for \alpha
< \frac{1}{1+2\zeta}, the limiting distribution is Gaussian. For \alpha 
 > 2 the
limiting distribution will be shown to be equal to the limiting 
distribution of
the loop erased walk.


http://front.math.ucdavis.edu/math.PR/0411551

---------------------------------------------------------------

3055. EXACT VARIATIONS FOR STOCHASTIC HEAT EQUATIONS DRIVEN BY 
SPACE--TIME  WHITE NOISE

Jan Pospisil and Roger Tribe

This paper calculates the exact quadratic variation in space and quartic
variation in time for the solutions to a one dimensional stochastic heat
equation driven by a multiplicative space-time white noise.


http://front.math.ucdavis.edu/math.PR/0411552

---------------------------------------------------------------

3056. COMPACTNESS OF THE LIMIT SET IN FIRST-PASSAGE PERCOLATION ON 
VORONOI  TILINGS

Leandro P.R. Pimentel

In this paper we consider first-passage percolation models on Voronoi 
tilings
of the plane and present a sufficient condition for the compactness of 
the
limit set. This result is based on a static renormalization technique 
and also
provide an inequality involving critical probabilities for bond 
percolation
models.


http://front.math.ucdavis.edu/math.PR/0411560

---------------------------------------------------------------

3057. COMPETING GROWTH AND GEODESICS IN FIRST-PASSAGE PERCOLATION

Leandro P.R. Pimentel

We consider a competing spatial growth dynamics permitting that more 
than one
cluster develop in the same environment given by a first-passage 
percolation
model on a Voronoi tiling of the plane. We focus on the long time 
behavior of
these competing clusters and derive some limit theorems related to the
morphology of the ``competition interface''. To study the structure of 
this
interface we use the notion of geodesic in first-passage percolation and
explore the coalescence behavior of semi-infinite geodesics with the 
same
orientation.


http://front.math.ucdavis.edu/math.PR/0411583

---------------------------------------------------------------

3058. A SHARP ISOPERIMETRIC BOUND FOR CONVEX BODIES

Ravi Montenegro

We consider the problem of lower bounding a generalized Minkowski 
measure of
subsets of a convex body with a log-concave probability measure, 
conditioned on
the set size. A bound is given in terms of diameter and set size, which 
is
sharp for all set sizes, dimensions, and norms. In the case of uniform 
density
a stronger theorem is shown which is also sharp.


http://front.math.ucdavis.edu/math.FA/0411018

---------------------------------------------------------------

3059. ON EXPONENTIAL STABILITY OF THE NONLINEAR FILTER FOR SLOWLY 
SWITCHING  MARKOV CHAINS

P. Chigansky

Exponential stability of the nonlinear filtering recursion is 
revisited, when
the signal is a finite state Markov chain. An asymptotic upper bound 
for the
filtering error due to incorrect initial condition is derived for the 
case of
slowly switching signal.


http://front.math.ucdavis.edu/math.PR/0411596

---------------------------------------------------------------

3060. THE QUANTIZATION COMPLEXITY OF DIFFUSION PROCESSES

Steffen Dereich

We investigate the high resolution coding problem for solutions of 
stochastic
differential equations in the L^p[0,1]- and the C[0,1]-space. Tight 
asymptotic
estimates are found under weak regularity assumptions. The main 
technical tool
is a decoupling method which allows us to relate the complexity of the
diffusion process to that of the Wiener process under certain random
distortions.


http://front.math.ucdavis.edu/math.PR/0411597

---------------------------------------------------------------

3061. AN ALMOST SURE INVARIANCE PRINCIPLE FOR RANDOM WALKS IN A 
SPACE-TIME  RANDOM ENVIRONMENT

F. Rassoul-Agha and T. Seppalainen

We consider a discrete time random walk in a space-time i.i.d. random
environment. We use a martingale approach to show that the walk is 
diffusive in
almost every fixed environment. We improve on existing results by 
proving an
invariance principle and considering environments with an annealed 
$L^2$ drift.
We also state an a.s. invariance principle for random walks in general 
random
environments whose hypothesis requires a subdiffusive bound on the 
variance of
the quenched mean, under an ergodic invariant measure for the 
environment
chain.


http://front.math.ucdavis.edu/math.PR/0411602

---------------------------------------------------------------

3062. AN ALMOST SURE INVARIANCE PRINCIPLE FOR ADDITIVE FUNCTIONALS OF 
MARKOV  CHAINS

F. Rassoul-Agha and T. Seppalainen

We prove an invariance principle for a vector-valued additive 
functional of a
Markov chain for almost every starting point with respect to an ergodic
equilibrium distribution. The hypothesis is a moment bound on the 
resolvent.


http://front.math.ucdavis.edu/math.PR/0411603

---------------------------------------------------------------

3063. NONCOMMUTATIVE CONTINUOUS BERNOULLI SHIFTS

J\"urgen Hellmich and  Claus K\"ostler and Burkhard K\"ummerer

We introduce a non-commutative extension of Tsirelson-Vershik's noises,
called (non-commutative) continuous Bernoulli shifts. These shifts 
encode
stochastic independence in terms of commuting squares, as they are 
familiar in
subfactor theory. Such shifts are, in particular, capable of producing
Arveson's product system of type I and type II. We investigate the 
structure of
these shifts and prove that the von Neumann algebra of a 
(scalar-expected)
continuous Bernoulli shift is either finite or of type III.
   The role of (`classical') stationary flows for Tsirelson-Vershik's 
noises is
now played by cocycles of continuous Bernoulli shifts. We show that 
these
cocycles provide an operator algebraic notion for Levy processes. They 
lead, in
particular, to units and `logarithms' of units in Arveson's product 
systems.
Furthermore, we introduce (non-commutative) white noises, which are 
operator
algebraic versions of Tsirelson's `classical' noises. We give examples 
coming
from probability, quantum probability and from Voiculescu's theory of 
free
probability.
   Our main result is a bijective correspondence between additive and 
unital
shift cocycles. For the proof of the correspondence we develop tools 
which are
of interest on their own: non-commutative extensions of stochastic Ito
integration, stochastic logarithms and exponentials.


http://front.math.ucdavis.edu/math.OA/0411565

---------------------------------------------------------------

3064. EXACT CONSTANTS IN THE ROSENTHAL MOMENT INEQUALITIES FOR SUMS OF  
INDEPENDENT CENTERED RANDOM VARIABLES

B. Naimark and  E. Ostrovsky

We study the exact constants in the moment inequalities for sums of 
centered
independent random variables: improve their asymptotics, low and upper 
bounds,
calculate more exact asymptotics, elaborate the numerical algorithm for 
their
calculation, study the class of smoothing etc.


http://front.math.ucdavis.edu/math.PR/0411614

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3065. EXPONENTIAL BOUNDS FOR RANDOM SUMS

B.M. Migdashiev and  E.I. Ostrovsky

We construct a non - improved exponential bounds for distribution of 
normed
sums of i.,i.d. random variables with random numbers of summand.


http://front.math.ucdavis.edu/math.PR/0411616

---------------------------------------------------------------

3066. LONG RANGE EXCLUSION PROCESSES, GENERATOR AND INVARIANT MEASURES

E. D. Andjel (Univ. Provence) and  H. Guiol (INP Grenoble)

We show that if $\mu$ is an invariant measure for the long range 
exclusion
process putting no mass on the full configuration, $L$ is the formal 
generator
of that process, and $f$ is a cylinder function, then $Lf 
\in\mathbf{L}^{1}
(d\mu)$ and $\int Lf d\mu =0$. This result is then applied to 
determine, i) the
set of invariant and translation invariant measures of the long range 
exclusion
process on $\Z^d$ when the underlying random walk is irreducible; ii) 
the set
of invariant measures of the long range exclusion process on $\Z$ when 
the
underlying random walk is irreducible and has either zero mean or 
allows jumps
only to the nearest neighbors.


http://front.math.ucdavis.edu/math.PR/0411655

---------------------------------------------------------------

3067. LARGE DEVIATIONS FOR TRAPPED INTERACTING BROWNIAN PARTICLES AND 
PATHS

Stefan Adams and  Jean-Bernard Bru and  Wolfgang Koenig

We introduce two probabilistic models for $N$ interacting Brownian 
motions
moving in a trap in $ \R^d $ under mutually repellent forces. The two 
models
are defined in terms of transformed path measures on finite time 
intervals
under a trap Hamiltonian and two respective pair-interaction 
Hamiltonians. The
first pair interaction exhibits a {\it particle} repellency, while the 
second
one imposes a {\it path} repellency.
   We analyse both models in the limit of diverging time with fixed 
number $ N $
of Brownian motions. In particular, we prove large deviations 
principles for
the normalised occupation measures. The minimisers of the rate 
functions are
related to the Hamilton operator for $ N $ interacting trapped 
particles. More
precisely, in the particle-repellency model, the minimiser is its 
ground state,
and in the path-repellency model, the minimisers are its ground 
product-states.
   This study is a contribution to the search for a mathematical 
formulation of
the quantum system of $ N $ trapped interacting bosons as a model for 
{\it
Bose-Einstein condensation}, motivated by the success of the famous 1995
experiments. Recently, Lieb, et al. described the large-N behaviour of 
the
ground state in terms of the well-known {\it Gross-Pitaevskii} formula,
involving the scattering length of the pair potential. We prove that the
large-N behaviour of the ground product-states is also described by the
Gross-Pitaevskii formula, however with the scattering length of the pair
potential replaced by its integral.


http://front.math.ucdavis.edu/math.PR/0411660

---------------------------------------------------------------

3068. DEFINITION OF A DETERMINISTIC BAYESIAN LOGIC

Frederic Dambreville (DGA/CTA/DT/GIP)

The Bayesian logic is generally associated to the definition of a prior
probabilistic law. Conditional algebra have been investigated by some 
authors
though, but somehow the background framework is still probabilistic and 
the
entire logic is not specified. In this paper, the definition of a 
Deterministic
Bayesian Logic is proposed. This logic is completely independent of any 
notion
of probability. The coherence of this logic is proven and various 
logical
theorems are derived. It is shown that this logic is probabilizable and 
avoids
the negative result of Lewis. At last the probabilistic Bayesian rule is
recovered by posteriorly probabilizing our logic.


http://front.math.ucdavis.edu/cs.LO/0411097

---------------------------------------------------------------

3069. THE PEARCEY PROCESS

Craig A. Tracy and Harold Widom

The extended Airy kernel describes the space-time correlation functions 
for
the Airy process, which is the limiting process for a polynuclear 
growth model.
The Airy functions themselves are given by integrals in which the 
exponents
have a cubic singularity, arising from the coalescence of two saddle 
points in
an asymptotic analysis. Pearcey functions are given by integrals in 
which the
exponents have a quartic singularity, arising from the coalescence of 
three
saddle points. A corresponding Pearcey kernel appears in a random 
matrix model
and a Brownian motion model for a fix time. This paper derives an 
extended
Pearcey kernel by scaling the Brownian motion model at several times, 
and a
system of partial differential equations whose solution determines 
associated
distribution functions. We expect there to be a limiting nonstationary 
process
consisting of infinitely many paths, which we call the Pearcey process, 
whose
space-time correlation functions are expressible in terms of this 
extended
kernel.


http://front.math.ucdavis.edu/math.PR/0412005

---------------------------------------------------------------

3070. FREQUENTLY VISITED SETS FOR RANDOM WALKS

Endre Cs\'aki and  Ant\'onia F\"oldes and  P\'al R\'ev\'esz and  Jay 
Rosen and  Zhan  Shi

We study the occupation measure of various sets for a symmetric 
transient
random walk in $Z^d$ with finite variances. Let $\mu^X_n(A)$ denote the
occupation time of the set $A$ up to time $n$. It is shown that 
$\sup_{x\in
Z^d}\mu_n^X(x+A)/\log n$ tends to a finite limit as $n\to\infty$. The 
limit is
expressed in terms of the largest eigenvalue of a matrix involving the 
Green's
function of $X$ restricted to the set $A$. Some examples are discussed 
and the
connection to similar results for Brownian motion is given.


http://front.math.ucdavis.edu/math.PR/0412018

---------------------------------------------------------------

3071. CONVEX IMPRECISE PREVISIONS: BASIC ISSUES AND APPLICATIONS

Renato Pelessoni and  Paolo Vicig

In this paper we study two classes of imprecise previsions, which we 
termed
convex and centered convex previsions, in the framework of Walley's 
theory of
imprecise previsions. We show that convex previsions are related with a 
concept
of convex natural estension, which is useful in correcting a large 
class of
inconsistent imprecise probability assessments. This class is 
characterised by
a condition of avoiding unbounded sure loss. Convexity further provides 
a
conceptual framework for some uncertainty models and devices, like 
unnormalised
supremum preserving functions. Centered convex previsions are 
intermediate
between coherent previsions and previsions avoiding sure loss, and 
their not
requiring positive homogeneity is a relevant feature for potential
applications. Finally, we show how these concepts can be applied in 
(financial)
risk measurement.


http://front.math.ucdavis.edu/math.PR/0412030

---------------------------------------------------------------

3072. A PROBABILISTIC REPRESENTATION OF SOLUTIONS OF THE INCOMPRESSIBLE 
  NAVIER-STOKES EQUATIONS IN R3

M. Ossiander

A new probabilistic representation is presented for solutions of the
incompressible Navier-Stokes equations in 3 dimensions with given 
forcing and
initial velocity. This representation expresses solutions as scaled 
conditional
expectations of functionals of a Markov process indexed by the nodes of 
a
binary tree. It gives existence and uniqueness of weak solutions for 
all time
under relatively simple conditions on the forcing and initial data. 
These
conditions involve comparison of the forcing and initial data with 
majorizing
kernels.


http://front.math.ucdavis.edu/math.PR/0412034

---------------------------------------------------------------

3073. BENFORD'S LAW, VALUES OF L-FUNCTIONS AND THE 3X+1 PROBLEM

Alex V. Kontorovich and Steven J. Miller

We show the leading digits of a variety of systems satisfying certain
conditions follow Benford's Law. For each system proving this involves 
two main
ingredients. One is a structure theorem of the limiting distribution, 
specific
to the system. The other is a general technique of applying Poisson 
Summation
to the limiting distribution. We show the distribution of values of 
L-functions
near the central line and (in some sense) the iterates of the 3x+1 
Problem are
Benford.


http://front.math.ucdavis.edu/math.NT/0412003