Gibbs Measures and Phase Transitions on Sparse Random Graphs (2009)
Dembo, Amir, Montanari, Andrea
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite)...
Amir Dembo, Alain-sol Sznitman
We study the asymptotic behavior for large N of the disconnection time TN of simple random walk on the discrete cylinder (Z/NZ) d × Z. When d is sufficiently large, we are able to substantially...
Spectral measure of heavy tailed band and covariance random matrices (2008)
Belinschi, Serban, Dembo, Amir, Guionnet, Alice
We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure $\mu$ of large random real symmetric matrices with heavy tailed entries. Specifically, consider...
Ising models on locally tree-like graphs (2008)
Dembo, Amir, Montanari, Andrea
We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that...
Cover times for Brownian motion and (2008)
Amir Dembo, Yuval Peres, Jay Rosen, Ofer Zeitouni
random walks in two dimensions
A Lower Bound on the Disconnection Time of a Discrete Cylinder (2008)
Amir Dembo, Alain-sol Sznitman
Abstract. We study the asymptotic behavior for large N of the disconnection time TN of simple random walk on the discrete cylinder (Z/NZ) d × Z. When d is sufficiently large, we are able to...
ON THE DISCONNECTION OF A DISCRETE CYLINDER BY A RANDOM (2008)
Amir Dembo, Alain-sol Sznitman
Abstract We investigate the large N behavior of the time the simple random walk on the discrete cylinder (ZZ=N ZZ)d \Theta ZZ needs to disconnect the discrete cylinder. We show that when d * 2, this...
Valleys and the maximum local time for random walk in random environment (2008)
Amir Dembo, Nina Gantert, Zhan Shi
Abstract Let,(n; x) be the local time at x for a recurrent one-dimensional random walk in random environment after n steps, and consider the maximum, \Lambda (n) = maxx,(n; x). It is known that lim...
On the Maximum Correlation Coefficient (2008)
Wlodzimierz Bryc, Amir Dembo, Abram Kagan
For an arbitrary random vector (X; Y ) and an independent random variable Z it is shown that the maximum correlation coefficient between X and Y + Z as a function of is lower semi-continuous...
1.1. Probability spaces and σ-fields 7 1.2. Random variables and their expectation 10
Ising models on locally tree-like graphs (2008)
Abstract We consider Ising models on graphs that converge locally to trees. Examples include random regulargraphs with bounded degree and uniformly random graphs with bounded average degree. We prove...
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...
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....
Large and Moderate Deviations for Hotelling's T-squared Statistic (2007)
. Let X;X 1 ; X 2 ; ::: be i.i.d. R d -valued random variables. We prove large and moderate deviations for Hotelling's T 2 -statistic when X is in the generalized domain of attraction of the...
Self-Normalized Moderate And Large Deviations (2007)
. Let fX n ; n 1g be i.i.d. R d -valued random variables. We prove Partial Large Deviation Principles (PLDP) for self-normalized partial sums with minimal or no moment assumptions, for both moderate...
Self-Normalized Large Deviations In Vector Spaces (2007)
. In this short note we define and study properties of Partial Large Deviation Principles (PLDP), using them to extend Cram'er's theorem to self-normalized partial sums of i.i.d. random...
Cover Time and Favourite Points for Planar Random Walks (2007)
Amir Dembo, Summary Christine Fricker
In this talk, Amir Dembo considers random walks on Z 2 and presents a proof of the Erd}os{ Taylor conjecture related to frequently covered points. The Kesten{Revesz conjecture on the covering time of...
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...
Amir Dembo, Jean-dominique Deuschel, Darrell Duffie
Abstract: This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default...
Refined Gibbs Conditioning Principle for Certain Infinite Dimensional Statistics (2007)
A. Dembo, J. Kuelbs, Amir Dembo, Jim Kuelbs
2 Let X 1; X 2; X 3; : : : be independent, identically distributed random observations taking values in a Polish space \Sigma, and ` a statistic on \Sigma with values in a separable Banach space E....
Moderate deviations for the blockwise bootstrap (2007)
Abbreviated title: Moderate deviations for blockwise bootstrap We study the moderate deviations for the empirical process of the blockwise bootstrap estimator for stationary sequences. In this...
Centro de Investigaci'on en Matem'aticas (2007)
Amir Dembo, Tim Zajic, Gamma P [nt
Uniform large and moderate deviations for functional empirical processes.
n) or O(log n). We show it is always O( (2007)
Amir Dembo, Ioannis Kontoyiannis
Abstract|The following critical phenomenon was recently discovered. When a memoryless source is compressed using a variable-length xed-distortion code, the fastest convergence rate of the (pointwise)...
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...
Amir Dembo, Ecole Normale, Superieure Lyon, Ofer Zeitouni
properties of Sinai's model of random walk in random environment
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...
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...
Let M(N) be a sequence of integers with M!1 as N!1 and M = o(N). For bounded i.i.d. r.v. k i and bounded i.i.d. r.v. i, we study the large deviation of the family of (ordered) scalar products X
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...
Moderate deviations for the blockwise bootstrap (2007)
Abbreviated title: Moderate deviations for blockwise bootstrap We study the moderate deviations for the empirical process of the blockwise bootstrap estimator for stationary sequences. In this...
The Patched Brownian Motion Distribution (2007)
Amir Dembo And, Amir Dembo, Xin Guo
Let W t be a standard Brownian motion. Consider a stochastic process X t such that dX t = (X t )dt + (X t )dW t , where (x) = min(x=a; 1) and a is a constant. In other words, the sample path of X t...
Markovian perturbation, response and fluctuation dissipation theorem (2007)
Dembo, Amir, Deuschel, Jean-Dominique
We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of ``linear response function'' in the general framework of...
Finite size scaling for the core of large random hypergraphs (2007)
Dembo, Amir, Montanari, Andrea
The (two) core of a hypergraph is the maximal collection of hyperedges within which no vertex appears only once. It is of importance in tasks such as efficiently solving a large linear system over...
A Lower Bound on the Disconnection Time of a Discrete Cylinder (2007)
Dembo, Amir, Sznitman, Alain-Sol
We study the asymptotic behavior for large N of the disconnection time T_N of simple random walk on a discrete cylinder with base a d-dimensional discrete torus of side-length N. When d is...
On the Relation of Anticipative Stratonovich and Symmetric Integrals: A Decomposition Formula (2007)
Prepared in cooperation with Stanford University, Stanford, CA.
Finite size scaling for the core of large random hypergraphs (2007)
The (two) core of an hyper-graph is the maximal collection of hyper-edges within which no vertex appears only once. It is of importance in tasks such as efficiently solving a large linear system over...
Finite size scaling for the core of large random hypergraphs (2007)
The (two) core of an hyper-graph is the maximal collection of hyper-edges within which no vertex appears only once. It is of importance in tasks such as efficiently solving a large linear system over...
Limiting dynamics for spherical models of spin glasses at high temperature (2006)
Dembo, Amir, Guionnet, Alice, Mazza, Christian
We analyze the coupled non-linear integro-differential equations whose solutions is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for...
Large and Moderate Deviations for Hotelling's T^2-Statistics (2006)
Dembo, Amir; Stanford University; Amir@stat.stanford.edu, Shao, Qi-Man; Hong Kong University Of Science And Technology; Maqmshao@ust.hk
Let X , X1, X 2 , ... be i.i.d. R d-valued random variables. We prove large and moderate deviations for Hotelling's T2-statistic when X is in the generalized domain of attraction of the normal...
Spectral measure of large random Hankel, Markov and Toeplitz matrices (2006)
Bryc, Włodzimierz, Dembo, Amir, Jiang, Tiefeng
We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel and Toeplitz matrices generated by i.i.d. random variables {Xk} of unit variance,...
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)...
Cugliandolo-Kurchan equations for dynamics of Spin-Glasses (2005)
Arous, Gerard Ben, Dembo, Amir, Guionnet, Alice
We study the Langevin dynamics for the family of spherical $p$-spin disordered mean-field models and prove that in the limit of system size $N$ approaching infinity, the empirical state correlation...
Valleys and the maximum local time for random walk in random environment (2005)
Dembo, Amir, Gantert, Nina, Peres, Yuval, Shi, Zhan
Let $\xi(n, x)$ be the local time at $x$ for a recurrent one-dimensional random walk in random environment after $n$ steps, and consider the maximum $\xi^*(n) = \max_x \xi(n,x)$. It is known that...
How large a disc is covered by a random walk in n steps? (2005)
Dembo, Amir, Peres, Yuval, Rosen, Jay
We show that the largest disc covered by a simple random walk (SRW) on $\mathbb{Z}^2$ after n steps has radius n^{1/4+o(1)}, thus resolving an open problem of R\'{e}v\'{e}sz [Random Walk in Random...
Incluye bibliografía e índice
Universal denoising for the finite-input-general-output channel (2005)
We consider the problem of reconstructing a finite-alphabet signal corrupted by a known memoryless channel with a general output alphabet. The goodness of the reconstruction is measured by a given...
Spectral Measure Of Large Random Hankel, (2005)
Markov And Toeplitz, W Lodzimierz Bryc, Amir Dembo, Tiefeng Jiang
We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure.
Universal denoising for the finite-input-general-output channel (2005)
We consider the problem of reconstructing a finite-alphabet signal corrupted by a known memoryless channel with a general output alphabet. The goodness of the reconstruction is measured by a given...
Cugliandolo-Kurchan equations for dynamics of Spin-Glasses (2004)
Arous, Gerard Ben, Dembo, Amir, Guionnet, Alice
We study the Langevin dynamics for the family of spherical $p$-spin disordered mean-field models and prove that in the limit of system size $N$ approaching infinity, the empirical state correlation...
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}...
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...
Cugliandolo-Kurchan equations for dynamics of Spin-Glasses (2004)
Arous, Gerard Ben, Dembo, Amir, Guionnet, Alice
We study the Langevin dynamics for the family of spherical $p$-spin disordered mean-field models and prove that in the limit of system size $N$ approaching infinity, the empirical state correlation...
Cugliandolo-Kurchan equations for dynamics of Spin-Glasses (2004)
Arous, Gerard Ben, Dembo, Amir, Guionnet, Alice
We study the Langevin dynamics for the family of spherical $p$-spin disordered mean-field models and prove that in the limit of system size $N$ approaching infinity, the empirical state correlation...
Brownian Motion on Compact Manifolds: Cover Time and Late Points (2003)
Dembo, Amir; Stanford University; Amir@math.stanford.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@earthlink.net
Let $M$ be a smooth, compact, connected Riemannian manifold of dimension $d>2$ and without boundary. Denote by $T(x,r)$ the hitting time of the ball of radius $r$ centered at $x$ by Brownian motion...
Spectral measure of large random Hankel, Markov and Toeplitz matrices (2003)
Bryc, Włodzimierz, Dembo, Amir, Jiang, Tiefeng
We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel and Toeplitz matrices generated by i.i.d. random variables $\{X_k\}$ of unit...
A large-deviation theorem for tree-indexed Markov chains (2003)
Dembo, Amir, Morters, Peter, Sheffield, Scott
Given a finite typed rooted tree $T$ with $n$ vertices, the {\em empirical subtree measure} is the uniform measure on the $n$ typed subtrees of $T$ formed by taking all descendants of a single...
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 $\alpha$,...
The Minimax Distortion Redundancy in Noisy Source Coding (2003)
Consider the problem of finite-rate filtering of a discrete memoryless process i#1 based on its noisy observation sequence i#1 , which is the output of a Discrete Memoryless Channel (DMC) whose input...
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...
Source coding, large deviations, and approximate pattern matching (2002)
Amir Dembo, Ioannis Kontoyiannis
Dedicated to the memory of Aaron Wyner, a valued friend and colleague. Abstract—In this review paper, we present a development of parts of rate-distortion theory and pattern-matching algorithms for...
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...
Source coding, large deviations, and approximate pattern matching (2002)
Amir Dembo, Ioannis Kontoyiannis
Dedicated to the memory of Aaron Wyner, a valued friend and colleague. Abstract—In this review paper, we present a development of parts of rate-distortion theory and pattern-matching algorithms for...
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...
Brownian Motion on Compact Manifolds: Cover Time and Late Points (2002)
Amir Dembo, Yuval Peres, Jay Rosen
Let M be a smooth, compact, connected Riemannian manifold of dimension d ≥ 3 and without boundary. Denote by T(x, ε) the hitting time of the ball of radius ε centered...
Amir Dembo, Jean-dominique Deuschel, Darrell Duffie
Abstract: This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default...
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...
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...
Remarks on the maximum correlation coefficient (2001)
Dembo, Amir, Kagan, Abram, Shepp, Lawrence A.
The maximum correlation coefficient between partial sums of independent and identically distributed random variables with finite second moment equals the classical (Pearson) correlation coefficient...
Greedy lattice animals: negative values and unconstrained maxima (2001)
Dembo, Amir, Gandolfi, Alberto, Kesten, Harry
Let $\{X_v, v \in \mathbb{Z}^d\}$ be i.i.d. random variables, and $S(\xi) = \sum_{v \in \xi} X_v$ be the weight of a lattice animal $\xi$. Let $N_n = \max\{S(\xi) : |\xi| = n$ \text{and $\xi$...
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...
Critical Behavior in Lossy Source Coding (2000)
Dembo, Amir, Kontoyiannis, Ioannis
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)...
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...
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...
Greedy Lattice Animals: Negative Values And Unconstrained Maxima (2000)
Amir Dembo, Alberto Gandolfi, Harry Kesten
. Let fX v ; v 2 Z d g be i.i.d. random variables, and S() = P v2 X v be the weight of a lattice animal . Let Nn = maxfS() : jj = n and contains the origing and Gn = maxfS() : [ n; n] d g. We show...
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...
Remarks on the Maximum Correlation Coefficient (2000)
Amir Dembo, Abram Kagan, Lawrence A. Shepp
The maximum correlation coefficient between partial sums of independent identically distributed random variables with finite second moment equals the classical (Pearson) correlation coefficient...
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...
The asymptotics of waiting times between stationary processes, allowing distortion (1999)
Dembo, Amir, Kontoyiannis, Ioannis
Given two independent realizations of the stationary processes $\mathbf{X} = {X_n;n \geq 1}$ and $\mathbf{Y} = {Y_n;n \geq 1}$, our main quantity of interest is the waiting time $W_n(D)$ until a...
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...
Ordered Overlaps in Disordered Mean-Field Models (1999)
Francis Comets, Amir Dembo, Gamma P N
Let M(N) a sequence of integers with M ! 1 as N ! 1 and M = o(N ). For bounded i.i.d. r.v. ¸ k i and bounded i.i.d. r.v. oe i , we study the large deviation of the family of (ordered) scalar...
The Asymptotics of Waiting Times Between Stationary Processes, Allowing Distortion (1999)
Amir Dembo, Ioannis Kontoyiannis
this paper is to extend these asymptotic results to W n (D) (see Corollaries 1 through 4, below). Little has been done in this direction: Recently, Yang and Kieffer (1998) showed that (2) holds for W...
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...
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...
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...
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...
Information inequalities and concentration of measure (1997)
We derive inequalities of the form $\Delta (P, Q) \leq H(P|R) + H(Q|R)$ which hold for every choice of probability measures P, Q, R, where $H(P|R)$ denotes the relative entropy of $P$ with respect to...
Information inequalities and concentration of measure (1997)
Abstract We derive inequalities of the form \Delta(P; Q) H(P jR) + H(QjR) which hold for every choice of probability measures P; Q; R, where H(P jR) denotes the relative entropy of P with respect to...
Large deviations for quadratic functionals of Gaussian processes (1997)
The Large Deviation Principle is derived for several unbounded additive functionals of centered stationary Gaussian processes. For example, the rate function corresponding to 1 T T 0 X2 t dt is 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...
Moderate Deviations for Martingales with Bounded Jumps (1996)
Dembo, Amir; Stanford University; Amir@math.stanford.edu
We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled,...
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...
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...
Information Inequalities and Concentration of Measure (1996)
We derive inequalities of the form \Delta(P; Q) H(P jR) + H(QjR) which hold for every choice of probability measures P; Q; R, where H(P jR) denotes the relative entropy of P with respect to R and...
On large deviations of empirical measures for stationary Gaussian processes (1995)
We show that the Large Deviation Principle with respect to the weak topology holds for the empirical measure of any stationary continuous time Gaussian process with continuous vanishing at infinity...
Uniform Large and Moderate Deviations for Functional Empirical Processes. (1995)
Amir Dembo, Tim Zajic, Gamma P [nt
For fX i g i1 a sequence of i.i.d. random variables taking values in a Polish space \Sigma with distribution ¯, we obtain large and moderate deviation principles for the processes fn \Gamma1 P [nt]...
On large deviations of empirical measures for stationary Gaussian processes (1995)
We show that the Large Deviation Principle with respect to the weak topology holds for the empirical measure of any stationary continuous time Gaussian process with continuous vanishing at infinity...
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 ;...
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...
Large Deviations and Strong Mixing (1993)
The Large Deviation Principle (LDP) with respect to the ø-topology holds for the empirical measure of any ff-mixing or any OE-mixing stationary process with a hyperexponential mixing rate of at...
Large Deviations and Strong Mixing (1993)
The Large Deviation Principle (LDP) with respect to the ø-topology holds for the empirical measure of any ff-mixing or any OE-mixing stationary process with a hyperexponential mixing rate of at...
Large deviations and strong mixing (1993)
Résumé Nous prouvons le propriétés de grandes déviations (P.G.D.) pour les mesures empiriques en τ-topologie, dans les cas de suites stationnaires sous conditions de mélange α(n) ≪...
If for a ‘permissible ’ family of functions F and an i.i.d. process {Xi} ∞ i=0 lim n→ ∞ sup
Amir Dembo, Jean-Dominique Deuschel, Darrell Duffie
This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a...
Amir Dembo, Jean-Deominique Deuschel, Darrell Duffie
This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a...
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).
A note on uniform laws of averages for dependent processes
If for a [`]permissible' family of functions and an i.i.d. process {Xi}[infinity]i=0, with probability one, then the same holds for away absolutely regular (weakly Bernoulli) process having the same...
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...