Probability Abstracts 59

H. Bell, W. Bryc

Motivated by the theory of large deviations, we introduce a class of
non-negative non-linear functionals that have a variational "rate function"
representation.

brycw@math.uc.edu
Amir Dembo and Ioannis Kontoyiannis

The following critical phenomenon was recently discovered. When a memoryless
source is compressed using a variable-length fixed-distortion code, the fastest
convergence rate of the (pointwise) compression ratio to the optimal $R(D)$
bits/symbol is either $O(\sqrt{n})$ or $O(\log n)$. We show it is always
$O(\sqrt{n})$, except for discrete, uniformly distributed sources.

yiannis@stat.purdue.edu
Timo Seppalainen

We study aspects of the hydrodynamics of one-dimensional totally asymmetric
K-exclusion, building on the hydrodynamic limit of Seppalainen (1999). We prove
that the weak solution chosen by the particle system is the unique one with
maximal current past any fixed location. A uniqueness result is needed because
we can prove neither differentiability nor strict concavity of the flux
function, so we cannot use the Lax-Oleinik formula or jump conditions to define
entropy solutions. Next we prove laws of large numbers for a second class
particle in K-exclusion. The macroscopic trajectories of second class particles
are characteristics and shocks of the conservation law for the particle
density. In particular, we extend to K-exclusion Ferrari's result that the
second class particle follows a macroscopic shock in the Riemann solution. The
technical novelty of the proofs is a variational representation for the
position of a second class particle, in the context of the variational coupling
method.

seppalai@iastate.edu
Janusz Szczepanski

Investigations of complexity of sequences lead to important applications such
as effective data compression, testing of randomness, discriminating between
information sources and many others. In this paper we establish formulas
describing the distribution functions of random variables representing the
complexity of finite sequences introduced by Lempel and Ziv in 1976. We show
that the distribution functions depend in an affine way on the probabilities of
the so called "exact" sequences.

jszczepa@ippt.gov.pl
L.R.G. Fontes, M. Isopi, C.M. Newman

Let $\tau = (\tau_i : i \in \z)$ denote i.i.d. positive random variables with
common distribution $F$ and (conditional on $\tau$) let $X = (X_t : t\geq0,
X_0=0)$, be a continuous-time simple symmetric random walk on $\z$ with
inhomogeneous rates $(\tau_i^{-1} : i \in \z)$. When $F$ is in the domain of
attraction of a stable law of exponent $\a<1$ (so that $\E(\tau_i) = \infty$
and X is subdiffusive), we prove that $(X,\tau)$, suitably rescaled (in space
and time), converges to a natural (singular) diffusion $Z = (Z_t : t\geq0,
Z_0=0)$ with a random (discrete) speed measure $\rho$. The convergence is such
that the ``amount of localization'', $\E \sum_{i \in \z} [\P(X_t = i|\tau)]^2$
converges as $t \to \infty$ to $\E \sum_{z \in \r} [\P(Z_s = z|\rho)]^2 > 0$,
which is independent of $s>0$ because of scaling/self-similarity properties of
$(Z,\rho)$. The scaling properties of $(Z,\rho)$ are also closely related to
the ``aging'' of $(X,\tau)$. Our main technical result is a general convergence
criterion for localization and aging functionals of diffusions/walks $Y^{(\e)}$
with (nonrandom) speed measures $\me \to \mu$ (in a sufficiently strong sense).

isopi@mercurio.mat.uniroma1.it
A. Koukkous, H. Guiol

We consider an asymmetric zero range process in infinite volume with zero
mean and random jump rates starting from equilibrium. We investigate the large
deviations from the hydrodynamical limit of the empirical distribution of
particles and prove an upper and a lower bound for the large deviation
principle. Our main argument is based on a super-exponential estimate in
infinite volume. For this we extend to our case a method developed by Kipnis &
al. (1989) and Benois & al. (1995).

abdellatif.koukkous@univ-rouen.fr
Marian Grendar, jr and Marian Grendar

Concept of exponential family is generalized by simple and general
exponential form. Simple and general potential are introduced. Maximum Entropy
and Maximum Likelihood tasks are defined. ML task on the simple exponential
form and ME task on the simple potentials are proved to be complementary in
set-up and identical in solutions. ML task on the general exponential form and
ME task on the general potentials are weakly complementary, leading to the same
necessary conditions. A hypothesis about complementarity of ML and MiniMax
Entropy tasks and identity of their solutions, brought up by a special case
analytical as well as several numerical investigations, is suggested in this
case.
  MiniMax Ent can be viewed as a generalization of MaxEnt for parametric linear
inverse problems, and its complementarity with ML as yet another argument in
favor of Shannon's entropy criterion.

umergren@savba.sk
Francis Comets, Roberto Fernandez, Pablo A. Ferrari

We present a perfect simulation algorithm for stationary processes indexed by
Z, with summable memory decay. Depending on the decay, we construct the process
on finite or semi-infinite intervals, explicitly from an i.i.d. uniform
sequence. Even though the process has infinite memory, its value at time 0
depends only on a finite, but random, number of these uniform variables. The
algorithm is based on a recent regenerative construction of these measures by
Ferrari, Maass, Martinez and Ney. As applications, we discuss the perfect
simulation of binary autoregressions and Markov chains on the unit interval.

pablo@ime.usp.br
James Allen Fill, Mark L. Huber 

For many probability distributions of interest, it is quite difficult to
obtain samples efficiently. Often, Markov chains are employed to obtain
approximately random samples from these distributions. The primary drawback to
traditional Markov chain methods is that the mixing time of the chain is
usually unknown, which makes it impossible to determine how close the output
samples are to having the target distribution. Here we present a new protocol,
the randomness recycler (RR), that overcomes this difficulty. Unlike classical
Markov chain approaches, an RR-based algorithm creates samples drawn exactly
from the desired distribution. Other perfect sampling methods such as coupling
from the past use existing Markov chains, but RR does not use the traditional
Markov chain at all. While by no means universally useful, RR does apply to a
wide variety of problems. In restricted instances of certain problems, it gives
the first expected linear time algorithms for generating samples. Here we apply
RR to self-organizing lists, the Ising model, random independent sets, random
colorings, and the random cluster model.

mhuber@orie.cornell.edu
James Allen Fill, Motoya Machida 

A system (P_a: a in A) of probability measures on a common state space S
indexed by another index set A can be ``realized'' by a system (X_a: a in A) of
S-valued random variables on some probability space in such a way that each X_a
is distributed as P_a. Assuming that A and S are both partially ordered, we may
ask when the system (P_a: a in A) can be realized by a system (X_a: a in A)
with the monotonicity property that X_a <= X_b almost surely whenever a <= b.
When such a realization is possible, we call the system (P_a: a in A)
``realizably monotone.'' Such a system necessarily is stochastically monotone,
that is, satisfies P_a <= P_b in stochastic ordering whenever a <= b. In
general, stochastic monotonicity is not sufficient for realizable monotonicity.
However, for some particular choices of partial orderings in a finite state
setting, these two notions of monotonicity are equivalent. We develop an
inverse probability transform for a certain broad class of posets S, and use it
to explicitly construct a system (X_a: a in A) realizing the monotonicity of a
stochastically monotone system when the two notions of monotonicity are
equivalent.

machida@math.usu.edu
David J. Aldous 

The random assignment (or bipartite matching) problem studies the random
total cost A_n of the optimal assignment of each of n jobs to each of n
machines, where the costs of the n^2 possible job-machine matches has
exponential (mean 1) distribution. Mezard - Parisi (1987) used the replica
method from statistical physics to argue non-rigorously that EA_n converges to
zeta(2) = pi^2/6. Aldous (1992) identified the limit as the optimal solution of
a matching problem on an infinite tree. Continuing that approach, we construct
the optimal matching on the infinite tree. This yields a rigorous proof of the
zeta(2) limit and of the conjectured limit distribution of edge-costs and their
rank-orders in the optimal matching.

aldous@stat.berkeley.edu
Gregory F. Lawler, Oded Schramm, Wendelin Werner

In a series of recent preprints, we have proven that with probability one the
Hausdorff dimension on the outer boundary of planar Brownian motion is 4/3,
confirming a conjecture by Mandelbrot. It is also shown that the Hausdorff
dimension of the set of cut points is a.s. 3/4. The present paper is an
expository outline of the arguments involved in the proof of these and related
results.

schramm@microsoft.com
C. D. Howard and C. M. Newman

The metric $D_\alpha (q,q')$ on the set $Q$ of particle locations of a
homogeneous Poisson process on $R^d$, defined as the infimum of $(\sum_i |q_i -
q_{i+1}|^\alpha)^{1/\alpha}$ over sequences in $Q$ starting with $q$ and ending
with $q'$ (where $| . |$ denotes Euclidean distance) has nontrivial geodesics
when $\alpha > 1$. The cases $1 <\alpha < \infty$ are the Euclidean
first-passage percolation (FPP) models introduced earlier by the authors while
the geodesics in the case $\alpha = \infty$ are exactly the paths from the
Euclidean minimal spanning trees/forests of Aldous and Steele. We compare and
contrast results and conjectures for these two situations. New results for $1 <
\alpha < \infty$ (and any $d$) include inequalities on the fluctuation
exponents for the metric ($\chi \le 1/2$) and for the geodesics ($\xi \le 3/4$)
in strong enough versions to yield conclusions not yet obtained for lattice
FPP: almost surely, every semi-infinite geodesic has an asymptotic direction
and every direction has a semi-infinite geodesic (from every $q$). For $d=2$
and $2 le \alpha < \infty$, further results follow concerning spanning trees of
semi-infinite geodesics and related random surfaces.

newman@courant.nyu.edu
M.A. Lifshits

We prove a sufficient condition for almost sure limit 
theorem for sums of independent random vectors under 
minimal moment assumptions and extremely mild assumptions 
about normalizing sequences. We also provide an example 
which shows that our sufficient condition is nearly 
optimal, as well as another sufficient condition due to 
I.Berkes and H.Dehling. 

lifts@mail.rcom.ru

M.A. Lifshits

Almost sure limit theorem (ASLT) for a sequence of random 
variables $\{\z_k\}$ means that under a reasonable choice 
of the weights $b_k$, the empirical measures 
$$Q_n = {1\over \g} \sum_{k=1}^n b_k \delta_{\zeta_k} $$ 
almost surely weakly converge to a limit law $G$. We assume 
$\z_k$ to be a normalized value of discrete-time 
martingale. We show that weak limit theorem does not imply  
ASLT even under good moment assumptions (an effect 
impossible for sums of independent variables).
Our main result contains sufficient conditions for ASLT 
under assumptions very close to those used in weak limit 
theorems. An interesting new feature of this result - 
appearance of {\it random} limit measure $G$.

lifts@mail.rcom.ru

M.A. Lifshits and E.S. Stankevich

Let $S_k$ be the $k$-th partial sum of i.i.d. random 
variables $X_1, X_2,...$. Define ``empirical'' measures 
$$Q_n={1\over\log n}\sum_{k=1}^n {1\over k}\delta_{S_k/
\sqrt k}.$$ If $\E|X_1|^m<\infty$ for all $m>0$, then $Q_n$
satisfy strong large deviations principle, as M.Heck, 
P.March and T.Seppalainen have recently proved. We show 
that the moment assumptions are optimal in this statement.

lifts@mail.rcom.ru

A.L. Koldobsky and M.A. Lifshits  

We study the asymptotic behavior, as the dimension goes 
to infinity, of the volume of sections of the unit
balls of the spaces $\ell_q^n, 0 < q  \le \infty.$
We compute the precise asymptotics of the average volume
of central sections and then prove a concentration 
inequality of exponential type. For the case of non-central 
hyperplane sections of the cube, we prove a local limit 
theorem confirming the conjecture on the asymptotically 
Gaussian dependence of the volume of sections on the 
distance from the hyperplane to the origin. 
Our calculations are based on connections between volume 
and the Fourier transform. 

koldobsk@math.missouri.edu    lifts@mail.rcom.ru

M.A. Lifshits and W. Linde 

We consider compactness properties of Volterra integral 
operator $T: L_p(0,\infty) \to L_q(0,\infty)$ defined by
$$(T f)(s) =\rho(s)\int_0^s \psi(t) f(t) dt.$$ 
Under certain optimal integrability conditions on the 
kernels $\rho,\psi$, the entropy numbers $e_n(T)$  satisfy
$$c_1 ||\rho\psi||_r < \liminf_{n\to\infty} n e_n(T)
\le \limsup_{n\to\infty} n e_n(T) < c_2 ||\rho\psi||_r $$
where $1/r = 1- 1/p +1/q >0$.
We also obtain sharp estimates for the approximation 
numbers of the operator $T$, thus extending former results 
due to Edmunds et al.. The entropy estimates are applied to 
investigate the small ball behaviour of the weighted  
Wiener process $\rho W$ on $(0,\infty)$ i.e.
we describe the behaviour of probabilities 
$P(||\rho W||_q < u}$ as $u\to 0$.

lifts@mail.rcom.ru   lindew@minet.uni-jena.de

Aboubakar Maitournam

First we present the mean curvature motion which is called anisotropic diffusion of 
Alvarez-Guichard-Lions-Morel, and which is used in the image processing. Then we give 
and prove a result on the stochastic representation of the DPE which governs the 
anisotropic diffusion, by using one result of Karatzas-Shreve based on Feynman-Kac 
formulas. At last we deduce a probabilistic interpretation of
the mean curvature motion related to the microcalcifications detection. 
That stochastic representation permits an easy understanding of anisotropic diffusion 
and gives the possibility to simulate an image smoothed by such method.

amaitour@pasteur.fr maia@math-info.univ-paris5.fr
Paolo Dai Pra, Anna Maria Paganoni and Gustavo Posta

We consider nonconservative, reversible spin systems, with
unbounded discrete spins. We show that for a class of these
dynamics in a high temperature regime, the relative entropy with
respect to the equilibrium distribution decays exponentially in
time, although the logarithmic-Sobolev inequality fails. To this
end we prove a weaker modification of the logarithmic-Sobolev
inequality.

daipra@mate.polimi.it annap@mate.polimi.it guspos@mate.polimi.it
Andre Goldman and Pierre Calka

Denote by $\varphi_{C}(t)=\sum_{n \geq 1} e^{-\lambda_n t},
t>0$, the spectral function related to the Dirichlet 
laplacian for the typical cell $C$ of a Johnson-Mehl 
tessellation in $R^d$, $d\geq 2$. We show that the 
expectation $E \varphi_{C}(t), t>0$, is a functional of the 
convex hull of a standard $d$-dimensional Brownian bridge. 
This enables us to study the asymptotic behaviour of
$E \varphi_{C}(t)$, when $t \to 0^+,+\infty.$ In particular, 
we prove that for a two-dimensional Poisson-Voronoi 
tessellation the law of the first eigenvalue $\lambda_1$ of 
$C$ satisfies the asymptotic relation 
$\ln E e^{-t\lambda_1} \sim -t^{1/2}4\sqrt{\pi}j_0$, when 
$ t \to +\infty $, where $j_0$ is the first zero of the 
Bessel function $J_0$.

goldman@jonas.univ-lyon1.fr  calka@jonas.univ-lyon1.fr

N. Cancrini, F. Martinelli, C. Roberto

We consider a conservative stochastic 
spin exchange dynamics reversible with respect to the canonical Gibbs
measure of a lattice gas model. We assume that the corresponding grand
canonical measure satisfies a suitable strong mixing
condition. Following previous work by two of us for the spectral gap, we
provide an alternative and quite natural, from the physical point of
view, proof of the well known result of Yau stating that the logarithmic
Sobolev constant in a box of side $L$ grows like $L^2$

martin@mat.uniroma3.it
Peter Major and Gyula Pap

Let us consider a triangular array of random
vectors $(X_j^{(n)},Y_j^{(n)})$, $n=1,2,
\dots$, $1\le j\le k_n$, such that the first 
coordinates $X_j^{(n)}$ take their values
in a non-compact Lie group and the second 
coordinates $Y_j^{(n)}$ in a compact group. 
Let the random vectors $(X_j^{(n)},Y_j^{(n)}$ 
be independent for fixed $n$, but we
do not assume any (independence type) 
condition about the relation between the 
components of these vectors. We show under 
fairly general conditions that if both random
products $S_n=\prod_{j=1}^{k_n}X_j^{(n)}$ and
$T_n=\prod_{j=1}^{k_n} Y_j^{(n)}$ have a 
limit distribution, then also the random 
vectors $(S_n,T_n)$ converge in distribution 
as $n\to\infty$. Moreover, the non-compact 
and compact coordinates of a random vector 
with this limit distribution are independent.

major@renyi.hu
Jeffrey E. Steif

We give an elementary proof that the second coordinate
(the scenery process) of the T,T inverse--process 
associated to any mean zero  i.i.d. random walk on Z^d 
is not a finitary factor of an i.i.d. process. In 
particular, this yields an elementary proof that the 
basic T,T inverse--process is not finitarily isomorphic to 
a Bernoulli shift (the stronger fact that it is not 
Bernoulli was proved by Kalikow) as well as provides (using 
past work of den Hollander and the author) an elementary 
example, namely the T,T inverse--process in 5 dimensions, 
of a process which is weak Bernoulli by not a finitary 
factor of an i.i.d. process. An example of such a process 
was given earlier by del Junco and Rahe. The above holds 
true for arbitrary stationary recurrent random walks as 
well. On the other hand, if the random walk is Bernoulli 
and transient, the T,T inverse--process associated to it 
is also Bernoulli. Finally, we show that finitary factors 
of i.i.d. processes with finite expected coding volume 
satisfy certain notions of weak Bernoulli in higher 
dimensions which have been previously introduced and 
studied in the literature. In particular, this yields 
(using past work of van den Berg and the author) the fact 
that the Ising model is weak Bernoulli throughout the 
subcritical regime.

steif@math.gatech.edu

Steven N. Evans

Using the classical theory of symmetric functions, 
a general distributional limit theorem is established for
$U$--statistics constructed from a sequence of independent,
identically distributed random variables taking values
in a local field with zero characteristic.

evans@stat.berkeley.edu
Wenbo V. Li and Qi-Man Shao

This is a survey paper on the subject.
Contents
1. Introduction
2. Inequalities for Gaussian random elements
  2.1 Isoperimetric Inequalities
  2.2 Concentration and Deviation Inequalities
  2.3 Comparison Inequalities
  2.4 Correlation Inequalities
3. Small ball probabilities in general setting
  3.1 Measure of shifted small balls
  3.2 Precise Links with Metric Entropy
  3.3 Exponential Tauberian theorem
  3.4 Lower bound on supremum under entropy conditions
  3.5 Connections with $l$-Approximation Numbers
  3.6 A connection between small ball probabilities
4. Gaussian processes with index set $T \subset \R$
  4.1 Lower bounds
  4.2 Upper bounds
  4.3 Fractional Brownian motions
  4.4 Integrated fractional Brownian motions
5.Gaussian processes with index set $T\subset\R^d$, $d\ge 2$
  5.1 Levy's fractional Brownian motions
  5.2 Brownian sheets
6. The small ball constants
  6.1 Exact estimates in Hilbert space
  6.2 Exact value of  small ball constants
  6.3 Existence of small ball constants
7. Applications of small ball probabilities
  7.1 Chung's law of the iterated logarithm
  7.2 Lower limits for empirical processes
  7.3 Rates of convergence of Strassen's functional LIL
  7.4 Rates of convergence of Chung type functional LIL
  7.5 A Wichura type functional LIL
  7.6 Fractal Geometry for Gaussian random fields
  7.7 Metric entropy estimates
  7.8 Capacity in Wiener space
  7.9 Natural Rates of escape for infinite dimensional 
      Brownian motions
  7.10 Asymptotic evaluation of Laplace transform 
       for large time
  7.11 Onsager-Machlup functionals
  7.12 Random fractal laws of the iterated logarithm

wli@math.udel.edu  shao@uoregon.edu
Wenbo V. Li and Qi-Man Shao

Let $B_0, B_1, \cdots, B_n$ be independent standard 
Brownian motions, starting at $0$. We investigate 
the tail of the capture time 
$\tau_n = \inf \{ t > 0: B_i (t)-b_i = B_0 (t)  
\mbox{for some}  1 \le i \le n \} $ 
where $0 < b_i \le 1, 1 \le i \le n$. In particular, 
we have $E \tau_3 =\infty$ and $E \tau_5 < \infty$. 
Various generalizations are also studied.
The conjecture of Bramson and Griffeath (1991) that
$E \tau_4 < \infty$ is still open.

wli@math.udel.edu  shao@uoregon.edu
Wenbo V. LI

Consider the first exit time $\tau_D$ of (d+1)-dimensional 
Brownian motion from the unbounded open domain 
$D=\{ (x, y) \in \R^{d+1} : y > f(x), x \in \R^d \}$
starting at the point $(x_0, f(x_0)+1)\in \R^{d+1}$ 
for some $x_0 \in \R^d$, where the function $f(x)$ on 
$\R^d$ is convex and $f(x) \to \infty$ as
the Euclidean norm $|x| \to \infty$. 
Very general estimates for the asymptotics of 
$\log P(\tau_D >t)$ are given by using Gaussian techniques.
In particular, for $f(x)=\exp (|x|^p)$, $p >0$, 
$ \lim_{t\to\infty} 
t^{-1} (\log t)^{2/p} \log P(\tau_D>t)=-j^2_\nu /2$
where $\nu=(d-2)/2$ and $j_\nu$ is the smallest positive 
zero of the Bessel function $J_{\nu}$. 

wli@math.udel.edu
Armen H. Zemanian

It is shown that transfinite graphs can be generated through
two simple operations, called `appending a branch' and  
`inserting a branch,' applied to finite graphs infinitely 
many times.  In this way, transfinite graphs are natural 
extensions of conventional graphs.  Certain pathological 
transfinite graphs cannot be so obtained.  For those 
graphs that can, a specific procedure for obtaining them   
from an expanding sequence of finite subgraphs is
established.  That sequence of finite subgraphs 
determines a `nonstandard graph,' the sequence being  
a representative of an equivalence class of sequences 
of finite graphs modulo a chosen nonprincipal ultrafilter.
This mimics the definition of the hyperreal numbers 
as equivalence classes of sequences of real numbers.  
With such a nonstandard transfinite graph in hand, 
random walks on it can be obtained by considering random   
walks on a representative sequence of finite subgraphs.  
This allows us to lift many standard results into a   
nonstandard setting, but now probabilities are hyperreals.  
A typical result is that we can now quantify and compare   
infinitesimal escape probabilities from different nodes, 
thereby comparing probabilities of recurrence.  All the   
many restrictions needed to establish random walks on   
standard transfinite graphs are no longer required.

zeman@ee.sunysb.edu

P. Bleher, J. Ruiz, R. H. Schonmann, S. Shlosman and V. Zagrebnov

We discuss statistical mechanics on non-amenable graphs, and we study 
the features of the phase transition, which are due to non-amenability. 
For the Ising model on the usual lattice it is known that fluctuations 
of magnetization are much less likely in the states with non-zero 
magnetic field than in the pure states with zero field. We show that on 
the Cayley tree the corresponding fluctuations have the same order.

bleher@math.iupui.edu  ruiz@cpt.univ-mrs.fr  rhs@math.ucla.edu
 shlosman@cpt.univ-mrs.fr  zagrebnov@cpt.univ-mrs.fr
Krzysztof Burdzy and David Nualart

We investigate some aspects of the local time, parabolic 
measure and excursion theory of Brownian motion reflected 
on Brownian motion.

burdzy@math.washington.edu  nualart@mat.ub.es
Mathew D. Penrose and J. E. Yukich

Consider sequential packing of unit balls in a large cube,
as in the Renyi car-parking model, but in any dimension
and with finite input. We prove a law of large numbers 
and central limit theorem for the number of packed 
balls in the thermodynamic limit. We prove analogous
results for numerous related applied models,including
cooperative sequential adsorption, ballistic deposition,
and spatial birth-growth models. The proofs are based on
a general law of large numbers and central limit theorem 
for ``stabilizing''  functionals of marked point processes
of independent uniform points in a large cube, which are 
of independent interest. ``Stabilization''  means, loosely,
that local modifications have only local effects.

mathew.penrose@durham.ac.uk  joseph.yukich@lehigh.edu 

Mireille Chaleyat-Maurel and Marta Sanz-Sole

We consider the random vector $u(t,\underline
x)=(u(t,x_1),\dots,u(t,x_d))$, where $t>0,\ x_1,\dots,x_d$ are distinct
points of $\R^2$
and $u$ denotes the stochastic process solution to a stochastic wave
equation driven by
a noise white in time and correlated in space. In a recent paper by Millet
and Sanz-Solé
\cite{M/S-S2}, sufficient conditions are given ensuring existence and
smoothness of
density for $u(t,\underline x)$. We study here the positivity of such
density. Using
techniques developped in \cite{A-K-S} (see also \cite{M/S-S1}) based on
Analysis on an
abstract Wiener space, we characterize the set of points $y\in\R^d$ where
the density is
positive and we prove that, under suitable assumptions, the set is $\R^d$.

mcm@ccr.jussieu.fr

Probability Abstracts 59

1593. VARIATIONAL REPRESENTATIONS OF VARADHAN FUNCTIONALS

1594. CRITICAL BEHAVIOR IN LOSSY SOURCE CODING

1595. SECOND CLASS PARTICLES AS MICROSCOPIC CHARACTERISTICS IN TOTALLY ASYMMETRIC NEAREST-NEIGHBOR K-EXCLUSION PROCESSES

1596. ON THE DISTRIBUTION FUNCTION OF THE COMPLEXITY OF FINITE SEQUENCES

1597. RANDOM WALKS WITH STRONGLY INHOMOGENEOUS RATES AND SINGULAR DIFFUSIONS: CONVERGENCE, LOCALIZATION AND AGING IN ONE DIMENSION

1598. LARGE DEVIATIONS FOR A ZERO MEAN ASYMMETRIC ZERO RANGE PROCESS IN RANDOM MEDIA

1599. MINIMAX ENTROPY AND MAXIMUM LIKELIHOOD. COMPLEMENTARITY OF TASKS, IDENTITY OF SOLUTIONS

1600. PROCESSES WITH LONG MEMORY: REGENERATIVE CONSTRUCTION AND PERFECT SIMULATION

1601. THE RANDOMNESS RECYCLER: A NEW TECHNIQUE FOR PERFECT SAMPLING

1602. REALIZABLE MONOTONICITY AND INVERSE PROBABILITY TRANSFORM

1603. THE ZETA(2) LIMIT IN THE RANDOM ASSIGNMENT PROBLEM

1604. THE DIMENSION OF THE PLANAR BROWNIAN FRONTIER IS 4/3

1605. GEODESICS AND SPANNING TREES FOR EUCLIDEAN FIRST-PASSAGE PERCOLATION

1606. ALMOST SURE LIMIT THEOREM FOR SUMS OF RANDOM VECTORS

1607. ALMOST SURE LIMIT THEOREM FOR MARTINGALES

1608. ON THE LARGE DEVIATION PRINCIPLE FOR THE ALMOST SURE CLT

1609. AVERAGE VOLUMES OF SECTIONS OF CONVEX BODIES

1610. APPROXIMATION AND ENTROPY NUMBERS OF VOLTERRA OPERATORS WITH APPLICATION TO BROWNIAN MOTION

1611. MICROCALCIFICATIONS DETECTION AND STOCHASTIC REPRESENTATION OF ALVAREZ-GUICHARD-LIONS-MOREL ANISOTROPIC DIFFUSION DPE

1612. ENTROPY INEQULITIES FOR UNBOUNDED SPIN SYSTEMS

1613. ON THE SPECTRAL FUNCTION OF THE JOHNSON-MEHL AND POISSON-VORONOI CELLS

1614. THE LOGARITHMIC SOBOLEV CONSTANT OF KAWASAKI DYNAMICS UNDER A MIXING CONDITION REVISITED

1615. LIMIT THEOREMS ON THE DIRECT PRODUCT OF A NON-COMPACT LIE GROUP AND A COMPACT GROUP

1616. THE T,T INVERSE-PROCESS, FINITARY CODINGS AND WEAK BERNOULLI

1617. LOCAL FIELD U-STATISTICS

1618. GAUSSIAN PROCESSES: INEQUALITIES, SMALL BALL PROBABILITIES AND APPLICATIONS

1619. CAPTURE TIME OF BROWNIAN PURSUITS

1620. THE FIRST EXIT TIME OF BROWNIAN MOTION FROM UNBOUNDED DOMAIN

1621. NONSTANDARD TRANSFINITE GRAPHS AND RANDOM WALKS ON THEM

1622. RIGIDITY OF THE CRITICAL PHASES ON A CAYLEY TREE

1623. BROWNIAN MOTION REFLECTED ON BROWNIAN MOTION

1624. LIMIT THEORY FOR RANDOM SEQUENTIAL PACKING AND DEPOSITION

1625. POSITIVITY OF THE DENSITY FOR THE STOCHASTIC WAVE EQUATION IN TWO SPATIAL DIMENSIONS