Yilmaz, Atilla, Zeitouni, Ofer
We consider the quenched and averaged (or annealed) large deviation rate functions $I_q$ and $I_a$ for space-time and (the usual) space-only RWRE on $\mathbb{Z}^d$. By Jensen's inequality, $I_a\leq...
The single ring theorem (2009)
Guionnet, Alice, Krishnapur, Manjunath, Zeitouni, Ofer
We study the empirical measure $L_{A_n}$ of the eigenvalues of non-normal square matrices of the form $A_n=U_nD_nV_n$ with $U_n,V_n$ independent Haar distributed on the unitary group and $D_n$ real...
Deterministic approximation for the cover time of trees (2009)
We present a deterministic algorithm that given a tree T with n vertices, a starting vertex v and a slackness parameter epsilon > 0, estimates within an additive error of epsilon the cover and return...
Ecole Polytechnique Fédérale de Lausanne (2009)
Gérard Ben Arous, Département De Mathématiques, Ofer Zeitouni
Partially supported by a US-Israel BSF grant. Curvature driven flows have been extensively considered from a deterministic point of view. Besides their mathematical interest, they have been shown to...
Stephane Mallat, Ofer Zeitouni
September 4, 2000. General problem Let Y: = (Y1; : : : ; YN) denote an N-dimensional Gaussian vector with independent zero mean components of variance oei = E(Y 2i). We assume for concreteness that...
Peterson, Jonathon, Zeitouni, Ofer
We derive properties of the rate function in Varadhan's (annealed) large deviation principle for multidimensional, ballistic random walk in random environment, in a certain neighborhood of the zero...
SHORTEST SPANNING TREES AND A COUNTEREXAMPLE FOR RANDOM WALKS IN RANDOM ENVIRONMENTS (2008)
Abstract. We construct forests spanning Z d, d ≥ 2, that are stationary and directed, and whose trees are infinite but are as short as possible. For d ≥ 3, two independent copies of such forests,...
Levy, Nathan, Zeitouni, Ofer, Shamai, Shlomo
We apply the theory of random Schr\"odinger operators to the analysis of multi-users communication channels similar to the Wyner model, that are characterized by short-range intra-cell broadcasting....
Levy, Nathan, Somekh, Oren, Shamai, Shlomo, Zeitouni, Ofer
In this paper we study the spectrum of certain large random Hermitian Jacobi matrices. These matrices are known to describe certain communication setups. In particular we are interested in an uplink...
HIGH DENSITY ASSOCIATIVE MEMORIES 1 (2008)
A class of high density associative memories is constructed, starting from a description of desired properties those should exhibit. These properties include high capacity, controllable basins of...
Cover times for Brownian motion and (2008)
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
random walks in two dimensions
A CLT FOR REGULARIZED SAMPLE COVARIANCE MATRICES (2008)
Greg W. Anderson, Ofer Zeitouni
Abstract. We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences,...
A CLT FOR REGULARIZED SAMPLE COVARIANCE MATRICES (2008)
Greg W. Anderson, Ofer Zeitouni
Abstract. We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences,...
A QUENCHED INVARIANCE PRINCIPLE FOR CERTAIN BALLISTIC RANDOM WALKS IN I.I.D. ENVIRONMENTS (2008)
Noam Berger, Ofer Zeitouni, P Q Zd
ABSTRACT. We prove that every random walk in i.i.d. environment in dimension greater than or equal to 4 that has an almost sure positive speed in a certain direction, an annealed invariance principle...
TIGHTNESS FOR THE MINIMAL DISPLACEMENT OF BRANCHING RANDOM WALK (2008)
Abstract. Recursion equations have been used to establish weak laws of large numbers for the minimal displacement of branching random walk in one dimension. Here, we use these equations to establish...
TIGHTNESS FOR A FAMILY OF RECURSIVE EQUATIONS (2008)
Abstract. In this paper, we study the tightness of solutions for a family of recursive equations. These equations arise naturally in the study of random walks on tree-like structures. Examples...
TIGHTNESS FOR A FAMILY OF RECURSIVE EQUATIONS (2008)
Abstract. In this paper, we study the tightness of solutions for a family of recursive equations. These equations arise naturally in the study of random walks on tree-like structures. Examples...
A CLT FOR REGULARIZED SAMPLE COVARIANCE MATRICES (2008)
Greg W. Anderson, Ofer Zeitouni
Abstract. We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences,...
TIGHTNESS FOR THE MINIMAL DISPLACEMENT OF BRANCHING RANDOM WALK (2008)
Abstract. Recursion equations have been used to establish weak laws of large numbers for the minimal displacement of branching random walk in one dimension. Here, we use these equations to establish...
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
Let (x; r) denote the occupation measure of the ball of radius r centered at x for Brownian motion fW t g 0t1 in IR d; d 2. We prove that for any analytic set E in [0; 1], we have inf t2E lim inf r!0...
A Large Deviations Analysis of Range Tracking Loops (2007)
Large deviations theory is applied to the analysis of a discrete time range tracking loop. It is shown that the resulting asymptotics differ from those of the continuous time diffusion limit. 1...
Optimality of the Karhunen-Loeve basis in nonlinear reconstruction (2007)
Stephane Mallat Ofer, Ofer Zeitouni
3.39> Y, where Y is already expressed in its Karhunen-Loeve basis, whereas other choices of correspond to an expansion in other, non K-L bases. Let T () 2 P if T () is composed only of zeroes and...
Exponential Rates for Error Probabilities in DMPSK Systems (2007)
Amir Dembo, Victor Galperin, Ofer Zeitouni
Precise analytical asymptotic exponential rates of error, and bounds on those rates, for differential multiple-phase-shift keying (DMPSK) systems that include post-detection integration are provided....
Uniform Decay and Equicontinuity for Normalized, Parameter Dependent, Ito Integrals (2007)
David Levanony Adam, Adam Shwartz, Ofer Zeitouni
Let fM t (`); t 0g `2IR d be a collection of continuous, continuous-time martingales such that for all t ? 0, the associated increasing processes satisfy ! M(`) ? t !1 as k`k !1. We show that if !...
Universitat Zurich, Technische Universitat Berlin and Technion (2007)
Ch Ni On, Erwin Bolthausen, Jean-dominique Deuschel, Ofer Zeitouni
. Consider the massless free field on the d-dimensional lattice Z d ; d 3; that is the centered Gaussian field on R Z d with covariances given by the Green function of the simple random walk on Z d ....
Ofer Zeitouni December, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX n g (called a...
Yuval Peres, Jay Rosen, Ofer Zeitouni
this paper, log 2 stands for the logarithm to the base 2.
Amir Dembo, Bjorn Poonen, Qi-man Shao, Ofer Zeitouni
Consider a polynomial of large degree n whose coecients are independent, identically distributed, non-degenerate random variables having zero mean and nite moments of all orders. We show that such a...
Quenched Large Deviations for one dimensional Nonlinear Filtering (2007)
Etienne Pardoux, Ofer Zeitouni, J Ir
Consider the standard, one dimensional, nonlinear ltering problem for diusion processes observed in small additive white noise: d t = ( t)dt + ( t)dB t; dY t = ( t)dt + "dV t; where B ; V...
Abstract We provide a mild mixing condition that carries the C.L.T. for normalized empirical means of centered stationary sequence of bounded random variables to the whole range of moderate...
Cover times for Brownian motion and random walks in two dimensions (2007)
Abstract. Let T (x; ") denote the rst hitting time of the disc of radius " centered at x for Brownian motion on the two dimensional torus T 2 We prove that sup x2T 2 T (x;...
Amir Dembo, Ecole Normale, Superieure Lyon, Ofer Zeitouni
properties of Sinai's model of random walk in random environment
Eddy Mayer-wolf, Ofer Zeitouni
Abstract. We consider Markov chains on the space of (countable) partitions of the interval [0; 1], obtained rst by size biased sampling twice (allowing repetitions) and then merging the parts with...
Amir Dembo, Yuval Peres, Ofer Zeitouni
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX k g (called a...
Yuval Peres, Jay Rosen, Ofer Zeitouni
Let T (x; r) denote the total occupation measure of the ball of radius r centered at x for Brownian motion in IR 3. We prove that sup jxj1 T (x; r)=(r 2 j log rj) ! 16= 2 a.s. as r! 0, thus solving a...
Amir Dembo, Bjorn Poonen, Qi-man Shao, Ofer Zeitouni
Consider a polynomial of large degree n whose coecients are independent, identically distributed, nondegenerate random variables having zero mean and nite moments of all orders. We show that such a...
Amir Dembo, Anatoly Vershik, St. Petersburg Branch, Ofer Zeitouni
Abstract We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation...
Concentration Of Permanent Estimators For Certain Large Matrices (2007)
Shmuel Friedland, B. Rider, Ofer Zeitouni
Let A n = (a ij ) i;j=1 be an n n positive matrix with entries in [a; b]; 0 < a b. Let X n = ( i;j=1 be a random matrix where fx ij g are i.i.d. N(0; 1) random variables. We show that for large n,...
Quenched Large Deviations for one dimensional Nonlinear Filtering (2007)
Étienne Pardoux, Etienne Pardoux, Ofer Zeitouni
Consider the standard, one dimensional, nonlinear ltering problem for diusion processes observed in small additive white noise: d t = ( t )dt + ( t )dB t ; dY t = ( t )dt + "dV t ; where B ; V...
We consider a Markov chain on the space of (countable) partitions of the interval [0; 1], obtained rst by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled...
Universites de Paris 6 Paris 7 - CNRS (UMR 7599) PR (2007)
Epublications Du Laboratoire, Paris Cnrs (umr, F. Comets, O. Zeitouni, Francis Comets, ...
We consider a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions. Continuing our previous work [2] for the law of...
Maximal Arithmetic Progressions in Random Subsets (2007)
Benjamini, Itai; Weizmann Institute Of Science; Itai.benjamini@weizmann.ac.il, Yadin, Ariel; Weizmann Institute Of Science; Ariel.yadin@weizmann.ac.il, Zeitouni, Ofer; University Of Minnesota; Zeitouni@math.umn.edu
Let U(N) denote the maximal length of arithmetic progressions in a random uniform subset of {0,1}N. By an application of the Chen-Stein method, we show that U(N)- 2 log(N)/log(2) converges in law to...
Maximal Arithmetic Progressions in Random Subsets (2007)
Benjamini, Itai, Yadin, Ariel, Zeitouni, Ofer
Let U(N) denote the maximal length of arithmetic progressions in a random uniform subset of {0,1}^N. By an application of the Chen-Stein method, we show that U(N)- 2 log(N)/log(2) converges in law to...
Quenched Limits for Transient, Zero Speed One-Dimensional Random Walk in Random Environment (2007)
Peterson, Jonathon, Zeitouni, Ofer
We consider a nearest-neighbor, one dimensional random walk $\{X_n\}_{n\geq 0}$ in a random i.i.d. environment, in the regime where the walk is transient but with zero speed, so that $X_n$ is of...
A quenched CLT for super-Brownian motion with random immigration (2007)
A quenched central limit theorem is derived for the super-Brownian motion with super-Brownian immigration, in dimension $d\geq 4$. At the critical dimension $d=4$, the quenched and annealed...
A quenched invariance principle for certain ballistic random walks in i.i.d. environments (2007)
We prove that every random walk in i.i.d. environment in dimension greater than or equal to 2 that has an almost sure positive speed in a certain direction, an annealed invariance principle and some...
Searching for a trail of evidence in a maze (2007)
Arias-Castro, Ery, Candès, Emmanuel J., Helgason, Hannes, Zeitouni, Ofer
Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting,...
Can One Decide the Type of the Mean from the Empirical Measure? (2007)
Kulkarni, Sanjeev R., Zeitouni, Ofer
The problem of deciding whether the mean of an unknown distribution is in a set Alpha or in its complement based on a sequence of independent random variables drawn according to this distribution is...
A Class of Adaptive Control Problems Solved via Stochastic Control (2007)
Following a set up investigated by Rishel we consider an adaptive control problem with unknown parameter x as a partially observed stochastic control problem. Exploiting the finite dimensionality of...
Lyapunov Exponents for Filtering Problems (2007)
Delyon, Bernard, Zeitouni, Ofer
The dependence of the optimal nonlinear filter on it's initial conditions is considered for continuous time linear filtering and for finite state space nonlinear filtering. Partial results are...
On the Onsager-Machlup Functional of Diffusion Processes Around Non C2 Curves (2007)
The Onsager Machlup function, namely the fictitious density of diffusions paths in function space is considered, where the density is evaluated around non-C2 curves, thus extending earlier results....
On the Relation of Anticipative Stratonovich and Symmetric Integrals: A Decomposition Formula (2007)
Prepared in cooperation with Stanford University, Stanford, CA.
Quenched Limits for Transient, Zero Speed One-Dimensional Random Walk in Random Environment (2007)
Jonathon Peterson, Ofer Zeitouni
We consider a nearest-neighbor, one dimensional random walk {Xn}n≥0 in a random i.i.d. environment, in the regime where the walk is transient but with zero speed, so that Xn is of order n s for...
Nathan Levy, Oren Somekh, Shlomo Shamai (shitz, Ofer Zeitouni
In this paper we study the spectrum of certain large random Hermitian Jacobi matrices. These matrices are known to describe certain communication setups. In particular we are interested in an uplink...
Quenched Limits for Transient, Zero Speed One-Dimensional Random Walk in Random Environment (2007)
Jonathon Peterson, Ofer Zeitouni
Abstract We consider a nearest-neighbor, one dimensional random walk {Xn}n>=0 in a random i.i.d.environment, in the regime where the walk is transient but with zero speed, so that Xn is of order...
Maximal Arithmetic Progressions in Random Subsets (2007)
Itai Benjamini, Ariel Yadin, Ofer Zeitouni
Let U (N) denote the maximal length of arithmetic progressions in a random uni-form subset of {0,1} N. By an application of the Chen-Stein method, we show that U (N) −2log N / log 2 converges in...
Nathan Levy, Oren Somekh, Shlomo Shamai (shitz, Ofer Zeitouni
In this paper we study the spectrum of certain large random Hermitian Jacobi matrices. These matrices are known to describe certain communication setups. In particular we are interested in an uplink...
A CLT for regularized sample covariance matrices (2006)
Anderson, Greg W., Zeitouni, Ofer
We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences, obtained by...
Tightness for a family of recursive equations (2006)
Bramson, Maury, Zeitouni, Ofer
In this paper, we study the tightness of solutions for a family of recursive equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the...
A law of large numbers for finite-range dependent random matrices (2006)
Anderson, Greg, Zeitouni, Ofer
We consider random hermitian matrices in which distant above-diagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by...
Multiscale analysis of exit distributions for random walks in random environments (2006)
Bolthausen, Erwin, Zeitouni, Ofer
We present a multiscale analysis for the exit measures from large balls in Z^d, d\geq 3, of random walks in certain i.i.d. random environments which are small perturbations of the fixed environment...
A Central Limit Theorem for biased random walks on Galton-Watson trees (2006)
Let ${\cal T}$ be a rooted Galton-Watson tree with offspring distribution $\{p_k\}$ that has $p_0=0$, mean $m=\sum kp_k>1$ and exponential tails. Consider the $\lambda$-biased random walk...
Shortest spanning trees and a counterexample for random walks in random environments (2006)
Bramson, Maury, Zeitouni, Ofer, Zerner, Martin P. W.
We construct forests that span ℤd, d≥2, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible. For d≥3, two...
Late points for random walks in two dimensions (2006)
Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer
Let $\mathcal{T}_{n}(x)$ denote the time of first visit of a point x on the lattice torus ℤn2=ℤ2/nℤ2 by the simple random walk. The size of the set of α, n-late points $\mathcal{L}_{n}(\alpha...
An extension of the "prior density for path" (Onsager-Machlup functional) is defined and shown to exist for Gaussian fields generated by solutions of elliptic Partial Differential Equations (PDEs)...
A General Classification Rule for Probability Measures (2006)
Zeitouni, Ofer, Kulkarni, Sanjeev R.
We consider the problem of classifying an unknown probability distribution based on a sequence of random samples drawn according to this distribution. Specifically, if A is a subset of the space of...
Random Walk in Dynamic Markovian Random Environment (2006)
Antar Bandyopadhyay, Ofer Zeitouni
We consider a model, introduced by Boldrighini, Minlos and Pellegrinotti [3, 4], of random walks in dynamical random environments on the integer lattice Z d with d ≥ 1. In this model, the...
An Invariance principle for Isotropic Diffusions in Random Environment (2006)
Alain-sol Sznitman, Ofer Zeitouni
We investigate in this work the asymptotic behavior of isotropic diffusions in random environment that are small perturbations of Brownian motion. When the space dimension is three or more, we prove...
Abstract. We consider random hermitian matrices in which distant abovediagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of...
Searching for a Trail of Evidence in a Maze (2006)
Ery Arias-castro, Emmanuel J. C, Hannes Helgason, Ofer Zeitouni
Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting,...
Abstract. We consider random hermitian matrices in which distant abovediagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of...
A Central Limit Theorem for biased random walks on Galton-Watson trees (2006)
Let T be a rooted Galton-Watson tree with offspring distribution {pk} that has p0 = 0, mean m = P kpk> 1 and exponential tails. Consider the λ-biased random walk {Xn}n≥0 on T; this is the...
A Central Limit Theorem for biased random walks on Galton-Watson trees (2006)
Let T be a rooted Galton-Watson tree with offspring distribution {pk} that has p0 = 0, mean m = P kpk> 1 and exponential tails. Consider the λ-biased random walk {Xn}n≥0 on T; this is the...
Random Walk in Dynamic Markovian Random Environment (2005)
Bandyopadhyay, Antar, Zeitouni, Ofer
We consider a model, introduced by Boldrighini, Minlos and Pellegrinotti, of random walks in dynamical random environments on the integer lattice Z^d with d>=1. In this model, the environment changes...
Shortest spanning trees and a counterexample for random walks in random environments (2005)
Bramson, Maury, Zeitouni, Ofer, Zerner, Martin P. W.
We construct forests that span $\mathbb{Z}^d$, $d\geq2$, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible....
A CLT for a band matrix model (2005)
Abstract. A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily...
A CLT for a band matrix model (2005)
Abstract. A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily...
A CLT for a band matrix model (2004)
Anderson, Greg, Zeitouni, Ofer
A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily...
Cover times for Brownian motion and random walks in two dimensions (2004)
Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer
Let $\TT(x,\eps)$ denote the first hitting time of the disc of radius $\eps$ centered at $x$ for Brownian motion on the two dimensional torus $\Bbb{T}^2$. We prove that $\sup_{x\in \Bbb{T}^2}...
Concentration of permanent estimators for certain large matrices (2004)
Friedland, Shmuel, Rider, Brian, Zeitouni, Ofer
Let An=(aij)i,j=1n be an n×n positive matrix with entries in [a,b], 0
Concentration of permanent estimators for certain large matrices (2004)
Friedland, Shmuel, Rider, Brian, Zeitouni, Ofer
Let A_n=(a_{ij})_{i,j=1}^n be an n\times n positive matrix with entries in [a,b], 0
A law of large numbers for random walks in random mixing environments (2004)
Comets, Francis, Zeitouni, Ofer
We prove a law of large numbers for a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the...
Diaconis, Persi, Mayer-Wolf, Eddy, Zeitouni, Ofer, Zerner, Martin P. W.
We consider a Markov chain on the space of (countable) partitions of the interval $[0,1]$, obtained first by size-biased sampling twice (allowing repetitions) and then merging the parts (if the...
Large deviations for random walk in random environment with holding times (2004)
Dembo, Amir, Gantert, Nina, Zeitouni, Ofer
Suppose that the integers are assigned the random variables $\{\omega_x,\mu_x\}$ (taking values in the unit interval times the space of probability measures on $\reals_+$), which serve as an...
Incluye bibliografía e índice
Random Walks in Random Environment (2004)
Abstract Random walks in random environments (RWRE's) have been a source of surprising phenomena and challenging problems since they began to be studied in the 70's. Hitting times and, more...
Persi Diaconis, Eddy Mayer-wolf, Ofer Zeitouni
transformations
Persi Diaconis, Eddy Mayer-wolf, Ofer Zeitouni
Dedicated to the memory of Bob Brooks (1952–2002) We consider a Markov chain on the space of (countable) partitions of the interval [0, 1], obtained first by size-biased sampling twice (allowing...
Shmuel Friedland, Brian Rider, Ofer Zeitouni
Let An = (aij) n i,j=1 be an n × n positive matrix with entries in [a,b], 0<a ≤ b. LetXn = ( √ aij xij) n i,j=1 be a random matrix, where {xij} are i.i.d. N(0, 1) random variables. We show...
Limit theorems for one-dimensional transient random walks in Markov environments (2003)
Mayer-Wolf, Eddy, Roitershtein, Alexander, Zeitouni, Ofer
We obtain non-Gaussian limit laws for one-dimensional random walk in a random environment assuming that the environment is a function of a stationary Markov process. This is an extension of the work...
Diaconis, Persi, Mayer-Wolf, Eddy, Zeitouni, Ofer, Zerner, Martin
We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled...
Random walks in random environments (2003)
Random walks in random environments (RWRE's) have been a source of surprising phenomena and challenging problems since they began to be studied in the 70's. Hitting times and, more recently, certain...
Late points for random walks in two dimensions (2003)
Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer
Let $\mathcal{T}_n(x)$ denote the time of first visit of a point $x$ on the lattice torus $\mathbb {Z}_n^2=\mathbb{Z}^2/n\mathbb{Z}^2$ by the simple random walk. The size of the set of $\alpha$,...
Concentration of Permanent Estimators for Certain Large Matrices (2003)
Shmuel Friedland, Brian Rider, Ofer Zeitouni
Let An = (a ij ) i;j=1 be an n n positive matrix with entries in [a; b]; 0 < a b. Let Xn = ( i;j=1 be a random matrix where fx ij g are i.i.d. N(0; 1) random variables. We show that for large n,...
A law of large numbers for random walks in random mixing environments (2003)
We prove a law of large numbers for a class of ballistic, multidimensional random walks in random environments where the environment satis es appropriate mixing conditions, which hold when the...
Quenched Large Deviations for one dimensional Nonlinear Filtering (2003)
Étienne Pardoux, Ofer Zeitouni
Consider the standard, one dimensional, nonlinear filtering problem for diffusion processes observed in small additive white noise: dXt = γ(Xt)dt + εdVt, where B·, V · are = b(Xt)dt + dBt, dY ε...
A law of large numbers for random walks in random mixing environments (2002)
Comets, Francis, Zeitouni, Ofer
We prove a law of large numbers for a class of multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a...
Mayer-Wolf, Eddy; Technion; Emw@tx.technion.ac.il, Zeitouni, Ofer; Technion; Zeitouni@ee.technion.ac.il, Zerner, Martin P.W.; Stanford University; Zerner@math.stanford.edu
We consider Markov chains on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with probability...
Mayer-Wolf, Eddy; Technion; Emw@tx.technion.ac.il, Zeitouni, Ofer; Technion; Zeitouni@ee.technion.ac.il, Zerner, Martin P.W.; Stanford University; Zerner@math.stanford.edu
We consider Markov chains on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with probability...
Large deviations for random walk in random environment with holding times, preprint (2002)
Amir Dembo, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned the random variables {ωx,µx} (taking values in the unit interval times the space of probability measures on R+), which serve as an environment. This...
Stochastic Approximations to Curve Shortening Flows via Particle Systems (2002)
Gerard Ben Arous, Allen Tannenbaum, Ecole Polytechnique Federale, Ofer Zeitouni
Curvature driven ows have been extensively considered from a deterministic point of view. Besides their mathematical interest, they have been shown to be useful for a number of applicatiions...
Random Walks in Random Environments (2002)
Random walks in random environments (RWRE's) have been a source of surprising phenomena and challenging problems since they began to be studied in the 70's. Hitting times and, more...
Cut Points And Diffusive Random Walks In Random Environment (2002)
Erwin Bolthausen, Alain-sol Sznitman, Ofer Zeitouni
We study in this work a special class of multi-dimensional random walks in random environment for which we are able to prove in a non-perturbative fashion both a law of large numbers and a functional...
Large Deviations for Random Walk in Random Environment with Holding Times (2002)
Amir Dembo, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned the random variables f! x ; x g (taking values in the unit interval times the space of probability measures on R+ ), which serve as an environment. This...
Large Deviations for Random Walk in Random Environment with Holding Times (2002)
Amir Dembo, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned random variables f! x ; x g (taking values in the unit interval times probability measures on R+ ), which serve as an environment. This environment de nes a...
Cover Times for Brownian Motion and Random Walks in Two Dimensions (2001)
Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer
Let T(x,r) denote the first hitting time of the disc of radius r centered at x for Brownian motion on the two dimensional torus. We prove that sup_{x} T(x,r)/|log r|^2 --> 2/pi as r --> 0. The same...
Aging properties of Sinai's model of random walk in random environment (2001)
Dembo, Amir, Guionnet, Alice, Zeitouni, Ofer
We study in this short note aging properties of Sinai's (nearest neighbour) random walk in random environment. With $\PP^o$ denoting the annealed law of the RWRE $X_n$, our main result is a full...
Mayer-Wolf, Eddy, Zeitouni, Ofer, Zerner, Martin P. W.
We consider Markov chains on the space of (countable) partitions of the interval $[0,1]$, obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with...
Thick points for intersections of planar sample paths (2001)
Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer
Let $L_n^{X}(x)$ denote the number of visits to $x \in {\bf Z}^2$ of the simple planar random walk $X$, up till step $n$. Let $X'$ be another simple planar random walk independent of $X$. We show...
Cover times for Brownian motion and random walks in two dimensions (2001)
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
Let T (x; ") denote the rst hitting time of the disc of radius " centered at x for Brownian motion on the two dimensional torus T 2 We prove that sup x2T 2 T (x; ")=j log...
Random polynomials having few or no real zeros (2000)
Dembo, Amir, Poonen, Bjorn, Shao, Qi-Man, Zeitouni, Ofer
Consider a polynomial of large degree n whose coefficients are independent, identically distributed, nondegenerate random variables having zero mean and finite moments of all orders. We show that...
Thick points for spatial Brownian motion: multifractal analysis of occupation measure (2000)
Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer
Let $\mathscr{T}(x,r)$ denote the total occupation measure of the ball of radius $r$ centered at $x$ for Brownian motion in $\mathbb{R}^3$. We prove that $\sup_{|x|\leq1}\mathscr{T}(x,r)/(r^{2}|\log...
Linear multiuser receivers in random environments (2000)
Abstract—We study the signal-to-interference (SIR) performance of linear multiuser receivers in random environments, where signals from the users arrive in “random directions. ” Such random...
Random Polynomials Having Few or No Real Zeros (2000)
Amir Dembo, Bjorn Poonen, Qi-man Shao, Ofer Zeitouni
Consider a polynomial of large degree n whose coecients are independent, identically distributed, nondegenerate random variables having zero mean and nite moments of all orders. We show that such a...
Random Polynomials Having Few or No Real Zeros (2000)
Amir Dembo, Bjorn Poonen, Qi-man Shao, Ofer Zeitouni
Consider a polynomial of large degree n whose coe#cients are independent, identically distributed, nondegenerate random variables having zero mean and finite moments of all orders. We show that such...
Linear Multiuser Receivers in Random Environments (2000)
We study the signal-to-interference (SIR) performance of linear multiuser receivers in random environments, where signals from the users arrive in "random directions". Such random...
Conditional Exponential Moments for Iterated Wiener Integrals (1999)
We provide sharp exponential moment bounds for (Stratonovich) iterated stochastic integrals under conditioning by certain small balls, including balls in certain Hölder-like norms of exponent...
Thick Points for Transient Symmetric Stable Processes (1999)
Dembo, Amir; Stanford University; Amir@stat.standford.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@idt.net, Zeitouni, Ofer; Technion; Zeitouni@ee.technion.ac.il
Let T(x,r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index $b<d$ in $R^d$ and K(b,d) denote the norm of the...
Thick Points for Transient Symmetric Stable Processes (1999)
Dembo, Amir; Stanford University; Amir@stat.standford.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@idt.net, Zeitouni, Ofer; Technion; Zeitouni@ee.technion.ac.il
Let T(x,r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index $b<d$ in $R^d$ and K(b,d) denote the norm of the...
\Lambda, Technion Haifa (1999)
Erwin Bolthausen, Jean Dominique Deuschel, Ofer Zeitouni
Absence of a wetting transition for a pinned harmonic crystal in dimensions three and larger
Abstract We provide sharp exponential moment bounds for (Stratonovich) iterated stochastic integrals under conditioning by certain small balls, including balls in certain HSlder-like norms of...
Thick points for transient symmetric stable processes, Elect (1999)
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
Let T (x; r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index in IR d and ;d denote the norm of the convolution with its...
Thick Points for Planar Brownian Motion and the Erdös-Taylor Conjecture on Random Walk (1999)
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
Let T (x; r) denote the occupation measure of the disc of radius r centered at x by planar Brownian motion run till time 1. We prove that sup jxj1 T (x; r)=(r 2 j log rj 2 ) ! 2 a.s. as r ! 0, thus...
Thick Points for Transient Symmetric Stable Processes (1999)
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
Let T (x, r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index # < d in IR d and # #,d denote the norm of the...
Information Estimates and Markov Random Fields (1999)
Consider a random eld, with values in some nite set IR and index set a cube n ZZ d . We show that in the vicinity (in the information-theoretic sense) of strongly mixing Markov elds, considering...
Francis Comets, Nina Gantert, Ofer Zeitouni
: Suppose that the integers are assigned random variables f! i g (taking values in the unit interval), which serve as an environment. This environment denes a random walk fXng (called a RWRE) which,...
On Increasing Subsequences Of I.I.D. Samples (1999)
Jean-dominique Deuschel, Ofer Zeitouni
. We study the fluctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and...
Conditional exponential moments for iterated Wiener integrals (1999)
We provide sharp exponential moment bounds for (Stratonovich) iterated stochastic integrals under conditioning by certain small balls, including balls in certain Holder-like norms of exponent greater...
We analyze the quasi-stationary distributions of the family of Markov chains fX n g; " > 0; obtained from small non-local random perturbations of iterates of a map f : I ! I on a compact...
Absence of a Wetting Transition for a Pinned Harmonic Crystal in Dimensions Three and Larger (1999)
Erwin Bolthausen, Jean Dominique Deuschel, Ofer Zeitouni
We consider a free lattice eld (a harmonic crystal) with a hard wall condition and a weak pinning to the wall. We prove that in a weak sense the pinning always dominates the entropic repulsion of the...
A Relaxation Model for Memory with High Storage Density. (1998)
Bachmann,Charles M., Cooper,Leon N., Dembo,Amir, Zeitouni,Ofer
A relaxation model is presented based on an N dimensional Coulomb potential. The model has arbitrarily large storage capacity and, in addition, well-defined basins of attraction about stored memory...
General Potential Surfaces and Neural Networks. (1998)
Investigating Hopfield's model of associative memory implementation by a neural network, led to a generalized potential system with a much superior performance as an associative memory. In...
Klebaner, Fima C., Lazar, Justin, Zeitouni, Ofer
We consider a Markov chain $X_n^{\varepsilon}$ obtained by adding small noise to a discrete time dynamical system and study the chain's quasi-stationary distribution (qsd). The dynamics are given by...
Thick Points for Spatial Brownian Motion: Multifractal Analysis of Occupation Measure (1998)
Amir Dembo Yuval, Yuval Peres, Jay Rosen, Ofer Zeitouni
Let T (x; r) denote the total occupation measure of the ball of radius r centered at x for Brownian motion in IR 3 . We prove that sup jxj1 T (x; r)=(r 2 j log rj) ! 16=ß 2 a.s. as r ! 0, thus...
Quenched Sub-Exponential Tail Estimates for One-Dimensional Random Walk in Random Environment (1998)
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX n g (called a...
Francis Comets, Nina Gantert, Ofer Zeitouni
: Suppose that the integers are assigned random variables f! i g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fXng (called a RWRE)...
Large Deviations for One-Dimensional Random Walk in a Random Environment - a Survey (1998)
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX n g (called a...
Robustness of Zakai's equation via Feynman-Kac representations (1998)
Rami Atar, Frederi Viens, Ofer Zeitouni
: We propose to study the sensitivity of the optimal filter to its initialization, by looking at the distance between two differently initialized filtering processes in terms of the ratio between two...
Large Deviations for Integer Partitions (1998)
Amir Dembo, Anatoly Vershik, St. Petersburg Branch, Ofer Zeitouni
We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation...
Robust Diffusion Approximation for Nonlinear Filtering (1998)
In this paper, we consider the filtering of diffusion processes observed in non-Gaussian noise, when diffusion approximations for the system apply. Standard continuity results show then that the...
Large Deviations for Integer Partitions (1998)
Amir Dembo, Anatoly Vershik, St. Petersburg Branch, Ofer Zeitouni
We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation...
Precise Large Deviation Estimates for One-Dimensional Random Walk in Random Environment (1998)
Agoston Pisztora, Tobias Povel, Ofer Zeitouni
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the interval [1/2,1)), which serve as an environment. This environment defines a random walk fX k g (called a...
Francis Comets, Nina Gantert, Ofer Zeitouni
: Suppose that the integers are assigned random variables f! i g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fXng (called a RWRE)...
Performance of Linear Multiuser Receivers in Random Environments (1998)
We study the SIR performance of linear multiuser receivers in random environments, where signals from the users arrive in "random directions". Such random environment may arise in a DS-CDMA...
Large Deviations for Integer Partitions (1998)
Amir Dembo, Anatoly Vershik T, St. Petersburg Branch, Ofer Zeitouni
We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation...
Francis Comets Nina, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned random variables f! i g (taking values in the unit interval), which serve as an environment. This environment de nes a random walk fXng (called a RWRE) which,...
Fima C. Klebaner, Justin Lazar, Ofer Zeitouni
We consider a Markov chain X ffl n obtained by adding small noise to a discrete time dynamical system and study the chain's quasi-stationary distribution (qsd). The dynamics is given by...
Robustness of Zakai's equation via Feynman-Kac representations (1997)
Rami Atar, Frederi Viens, Ofer Zeitouni
We propose to study the sensitivity of the optimal filter to its initialization, by looking at the distance between two differently initialized filtering processes in terms of the ratio between two...
Lyapunov Exponents For Finite State Nonlinear Filtering (1997)
. Consider the Wonham optimal filtering problem for a finite state ergodic Markov process in both discrete and continuous time, and let # be the noise intensity for the observation. We examine the...
Transportation Approach to Some Concentration Inequalities in Product Spaces (1996)
Dembo, Amir; Stanford University; Amir@math.stanford.edu, Zeitouni, Ofer; Technion - Israel Institute Of Technology; Zeitouni@ee.technion.ac.il
Let P be any product (Borel) probability measure on product (Polish) space E and for vectors x,y,z in E let f(x,y,z) be the number of coordinates k for which x_k neither equals y_k nor z_k. Using a...
Transportation Approach to Some Concentration Inequalities in Product Spaces (1996)
Using a transportation approach we prove that for every probability measures P; Q 1 ; Q 2 on N with P a product measure there exist r.c.p.d. j such that R j (jx)dP (x) = Q j () and Z dP (x) Z dP dQ 1...
Refinements of the Gibbs conditioning principle (1996)
Refinements of Sanov's large deviations theorem lead via Csisz'ar's information theoretic identity to refinements of the Gibbs conditioning principle which are valid for blocks whose...
Asymptotic filtering for finite state Markov chains (1996)
Rafail Khasminskii, Ofer Zeitouni
Asymptotic formulae for the optimal filtering error for finite state space Markov chains observed in independent noise are presented. Asymptotically optimal simple filters, which do not depend on the...
Exponential Stability for Nonlinear Filtering (1996)
We study the a.s. exponential stability of the optimal filter w.r.t. its initial conditions. A bound is provided on the exponential rate (equivalently, on the memory length of the filter) for a...
Variations On A Theme By Bismut (1996)
Daniel W. Stroock, Ofer Zeitouni, For C
. Let M be a compact, connected, Riemannian manifold of dimension d, let fP t : t ? 0g denote the Markov semigroups on C(M) determined by 1 2 \Delta, and let p t (x; y) denote the kernel (with...
Lyapunov Exponents for Finite State Nonlinear Filtering (1996)
Consider the Wonham optimal filtering problem for a finite state ergodic Markov process in both discrete and continuous time, and let oe be the noise intensity for the observation. We examine the...
A nonstandard form of the rate function for the occupation measure of a Markov chain (1996)
Paul Dupuis Division, Paul Dupuis, Ofer Zeitouni
We investigate, by means of an example, the large deviations principle for the empirical measure of a Markov chain when Feller continuity properties are not assumed. Using the weak convergence...
Transportation Approach to Some Concentration Inequalities in Product Spaces (1996)
Using a transportation approach we prove that for every probability measures P; Q 1 ; Q 2 on\Omega N with P a product measure there exist r.c.p.d. j such that R j (\Deltajx)dP (x) = Q j (\Delta) and...
Tail Estimates for One-Dimensional Random Walk in Random Environment (1996)
Amir Dembo, Yuval Peres, Ofer Zeitouni
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX k g (called a...
Tail Estimates for One-Dimensional Random Walk in Random Environment (1996)
Amir Dembo, Yuval Peres, Ofer Zeitouni
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX k g (called a...
Tail Estimates for One-Dimensional Random Walk in Random Environment (1996)
Amir Dembo, Yuval Peres, Ofer Zeitouni
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX k g (called a...
Refinements of the Gibbs conditioning principle (1996)
Refinements of Sanov's large deviations theorem lead via Csisz'ar's information theoretic identity to refinements of the Gibbs conditioning principle which are valid for blocks whose...
Limiting Curves for IID Records (1995)
Jean-Dominique Deuschel, Ofer Zeitouni
We consider the concentration of measure for n iid, two-dimensional random variables, under the conditioning that they form a record. Under mild conditions, we show that all random variables tend to...
On Roots of Random Polynomials (1995)
Ildar Ibragimov, Ofer Zeitouni
We study the distribution of the complex roots of random polynomials of degree n with i.i.d. coefficients. Using techniques related to Rice's treatment of the real roots question, we derive,...
Exact Behavior Of Gaussian Seminorms (1995)
Amir Dembo Eddy, Eddy Mayer--wolf, Ofer Zeitouni
The exact lower tail of Gaussian seminorms are evaluated, using a refinement of the techniques presented in [5]. KEYWORDS Gaussian norms. Large Deviations. AMS 1991 Subject Classification Primary...
On Roots of Random Polynomials (1995)
Ildar Ibragimov, Ofer Zeitouni
We study the distribution of the complex roots of random polynomials of degree n with i.i.d. coefficients. Using techniques related to Rice's treatment of the real roots question, we derive,...
Entropic Repulsion of the Lattice Free Field (1995)
Erwin Bolthausen, Jean-dominique Deuschel, Ofer Zeitouni
. Consider the massless free field on the d-dimensional lattice Z d ; d 3; that is the centered Gaussian field on R Z d with covariances given by the Green function of the simple random walk on Z d ....
A nonstandard form of the rate function for the occupation measure of a Markov chain (1995)
We investigate, by means of an example, the large deviations principle for the empirical measure of a Markov chain when Feller continuity properties are not assumed. Using the weak convergence...
Lyapunov Exponents for Finite State Nonlinear Filtering (1995)
Consider the Wonham optimal filtering problem for a finite state ergodic Markov process in both discrete and continuous time, and let oe be the noise intensity for the observation. We examine the...
Limiting Curves for IID Records (1995)
Jean-dominique Deuschel, Ofer Zeitouni
We consider the concentration of measure for n iid, two-dimensional random variables, under the conditioning that they form a record. Under mild conditions, we show that all random variables tend to...
Limit Distribution Of Maximal Non-Aligned Two-Sequence Segmental Score (1994)
Amir Dembo, Samuel Karlin, Ofer Zeitouni
Consider two independent sequences X 1 ; \Delta \Delta \Delta ; X n and Y 1 ; \Delta \Delta \Delta ; Y n . Suppose that X 1 ; \Delta \Delta \Delta ; X n are i.i.d. X and Y 1 ; \Delta \Delta \Delta ;...
The Exit Problem for a Class of Density Dependent Branching Systems (1994)
The influence of noise on a class of discrete time systems arising from models of density dependent branching processes is investigated. By considering iterates of the basic map, the time to escape...
Critical Phenomena for sequence matching with scoring (1994)
Amir Dembo, Samuel Karlin, Ofer Zeitouni
Consider two independent sequences X 1 ; \Delta \Delta \Delta ; X n and Y 1 ; \Delta \Delta \Delta ; Y n . Suppose that X 1 ; \Delta \Delta \Delta ; X n are i.i.d. X and Y 1 ; \Delta \Delta \Delta ;...
Large Deviations for Sub-Sampling From Individual Sequences (1994)
Consider a sequence of m deterministic points in IR d , and consider the empirical measure of a random sample (without replacements) of size n = n(m). We prove the large deviation principle and...
Large Deviations for Sub-Sampling From Individual Sequences (1994)
Consider a sequence of m deterministic points in IR d , and consider the empirical measure of a random sample (without replacements) of size n = n(m). We prove the large deviation principle and...
Large Exceedances for Multidimensional Lévy Processes (1993)
Amir Dembo, Samuel Karlin, Ofer Zeitouni
Three results on hitting a rare set by the increments of an IR d valued random process with stationary independent increments are presented: the first time that it occurs, the duration of such a...
The Probability Of Small Gaussian Ellipsoids And Associated Conditional Moments (1991)
Eddy Mayer Wolf, Ofer Zeitouni
The problem of computing the lower tail of a Gaussian norm is considered in this paper. Based on large deviations arguments, a bound on these tails is derived which is tighter than those obtained by...
The "prior density for path" (the Onsager-Machlup functional) is defined for solutions of semilinear elliptic type PDEs driven by white noise. The existence of this functional is proved by applying a...
Maximum a posteriori estimation of elliptic Gaussian fields observed via a noisy nonlinear channel
An extension of the "prior density for path" (Onsager-Machlup functional) is defined and shown to exist for Gaussian fields generated by solutions of elliptic PDEs driven by white noise. This...
Large deviations for subsampling from individual sequences
Consider a sequence of m deterministic points in ##R##d, and consider the empirical measure of a random sample (without replacements) of size n = n(m). We prove the large deviation principle and...
Exact behavior of Gaussian seminorms
Dembo, Amir, Mayer-Wolf, Eddy, Zeitouni, Ofer
The exact lower tail of Gaussian seminorms are evaluated, using a refinement of the techniques presented in Mayer-Wolf and Zeitouni (1993).
Can one decide the type of the mean from the empirical measure?
Kulkarni, Sanjeev R., Zeitouni, Ofer
The problem of deciding whether the mean of an unknown distribution is in a set A or in its complement based on a sequence of independent random variables drawn according to this distribution is...
Moderate Deviations for Iterates of Expanding Maps
Amir Dembo And, Amir Dembo, Ofer Zeitouni
We provide a mild mixing condition that carries the C.L.T. for normalized empirical means of centered stationary sequence of bounded random variables to the whole range of moderate deviations. It is...
Thin Points for Brownian Motion
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
Let T (x; r) denote the occupation measure of the ball of radius r centered at x for Brownian motion fW t g 0t1 in IR d ; d 2. We prove that for any analytic set E in [0; 1], we have inf t2E lim inf...
Moderate Deviations for Iterates of Expanding Maps
We provide a mild mixing condition that carries the C.L.T. for normalized empirical means of centered stationary sequence of bounded random variables to the whole range of moderate deviations. It is...
Thick Points for Transient Symmetric Stable Processes
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
Let T (x; r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index fi ! d in IR d and fi;d denote the norm of the convolution...
Thick Points for Spatial Brownian Motion: Multifractal Analysis of Occupation Measure
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
Let T (x; r) denote the total occupation measure of the ball of radius r centered at x for Brownian motion in IR 3 . We prove that sup jxj1 T (x; r)=(r 2 j log rj) ! 16=ß 2 a.s. as r ! 0, thus...