# Dembo, Amir

Overview
Works: 71 works in 169 publications in 1 language and 1,879 library holdings Conference papers and proceedings Author, Thesis advisor
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Most widely held works by Amir Dembo
Large deviations techniques and applications by Amir Dembo( Book )

43 editions published between 1992 and 2010 in English and held by 665 WorldCat member libraries worldwide

The theory of large deviations deals with the evaluation, for a family of probability measures parameterized by a real valued variable, of the probabilities of events which decay exponentially in the parameter. Originally developed in the context of statistical mechanics and of (random) dynamical systems, it proved to be a powerful tool in the analysis of systems where the combined effects of random perturbations lead to a behavior significantly different from the noiseless case. The volume complements the central elements of this theory with selected applications in communication and control systems, bio-molecular sequence analysis, hypothesis testing problems in statistics, and the Gibbs conditioning principle in statistical mechanics. Starting with the definition of the large deviation principle (LDP), the authors provide an overview of large deviation theorems in ${{\rm I\!R}}^d$ followed by their application. In a more abstract setup where the underlying variables take values in a topological space, the authors provide a collection of methods aimed at establishing the LDP, such as transformations of the LDP, relations between the LDP and Laplace's method for the evaluation for exponential integrals, properties of the LDP in topological vector spaces, and the behavior of the LDP under projective limits. They then turn to the study of the LDP for the sample paths of certain stochastic processes and the application of such LDP's to the problem of the exit of randomly perturbed solutions of differential equations from the domain of attraction of stable equilibria. They conclude with the LDP for the empirical measure of (discrete time) random processes: Sanov's theorem for the empirical measure of an i.i.d. sample, its extensions to Markov processes and mixing sequences and their application. The present soft cover edition is a corrected printing of the 1998 edition. Amir Dembo is a Professor of Mathematics and of Statistics at Stanford University. Ofer Zeitouni is a Professor of Mathematics at the Weizmann Institute of Science and at the University of Minnesota
Lectures on probability theory and statistics : Ecole d'Eté de Probabilités de Saint-Flour XXXII-2002 by Boris Tsirelson( Book )

28 editions published between 2004 and 2005 in English and held by 250 WorldCat member libraries worldwide

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Large portfolio losses by Amir Dembo( Book )

12 editions published in 2002 in English and held by 54 WorldCat member libraries worldwide

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 losses on a bank portfolio, or the total claims against an insurer. The results may be useful in allocating exposure limits, and in allocating risk capital across different lines of business. Assuming that, for a given total loss, the distress caused by the loss is larger if the loss occurs within a smaller time period, we provide a large-deviations estimate of the likelihood that there will exist a sub-period of the future planning period during which a total loss of the critical severity occurs. Under conditions, this calculation is reduced to the calculation of the likelihood of the same sized loss over a fixed initial time interval whose length is a property of the portfolio and the critical loss level
Large deviations and applications : the finite dimensional case by Amir Dembo( Book )

4 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide

These notes, which form the first chapter of a forthcoming book, are intended to serve as lecture notes on the topic of large deviations and applications for students whose background and interests are in applications which involve finite dimensional spaces. Although narrow in their scope, these notes present a good deal of the methods available for more general situations. A glaring omission is the method of sub-additivity, which will be discussed in another chapter in the book. Another deficiency of these notes is the sketchy bibliography and historical notes. We hope to correct this in the book
A large deviations analysis of range tracking loops by Amir Dembo( Book )

2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide

Lectures on Probability Theory and Statistics : Ecole d'Et? de Probabilit?s de Saint-Flour XXXIII - 2003 by Amir Dembo( )

3 editions published in 2005 in English and held by 3 WorldCat member libraries worldwide

This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo?s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki?s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques
Maximum a-posteriori estimation of random fields by Amir Dembo( Book )

2 editions published between 1988 and 1989 in English and held by 3 WorldCat member libraries worldwide

Sanov's theorem for sub-sampling from individual sequences by Amir Dembo( Book )

2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide

General Potential Surfaces and Neural Networks by Amir Dembo( Book )

3 editions published in 1987 in English and held by 2 WorldCat member libraries worldwide

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 particular, there are no spurious memories, and any set of desired points can be stored, with unlimited capacity (in the continuous time and real space version of the model). There are no limit cycles in this system, and the size of all basins of attraction can reach up to half the distance between the stored points, by proper choice of the design parameters. A discrete time version with its state space being the unit hypercube is also derived, and admits superior properties compared to the corresponding Hopfield network. In particular the capacity of any system of N neurons, with a fixed desired size of basins of attractions, is exponentially growing with N and is asymptotically optimal in the information theory sense. The computational complexity of this model is slightly larger than that of the Hopfield memory, but of the same order. The results are derived under an axiomatic approach which determines the desired properties and shows that the above mentioned model is the only one to achieve them
Large deviations for quadratic functionals of Gaussian processes by University of Minnesota( Book )

2 editions published in 1993 in English and held by 2 WorldCat member libraries worldwide

Maximum a-posteriori estimation of random fields : elliptic Gaussian fields observed via a noisy channel by Amir Dembo( Book )

2 editions published between 1988 and 1989 in English and held by 2 WorldCat member libraries worldwide

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) driven by white noise. This functional is then used to define and solve the MAP estimation of such fields observed via nonlinear noisy sensors. Existence results and a representation of the estimator are derived for this model
On large deviations of empirical measures for stationary Gaussian processes by Wlodzimierz Bryc( Book )

2 editions published between 1993 and 1994 in English and held by 2 WorldCat member libraries worldwide

Generalization of the window method for FIR digital filter design by Amir Dembo( Book )

2 editions published in 1983 in English and held by 2 WorldCat member libraries worldwide

On random determinants by Amir Dembo( Book )

3 editions published in 1987 in English and Undetermined and held by 2 WorldCat member libraries worldwide

Refinements of the gibbs conditioning principle by Amir Dembo( Book )

2 editions published in 1993 in English and held by 2 WorldCat member libraries worldwide

WMMSE design digital filter banks with specified composite response by Amir Dembo( Book )

1 edition published in 1985 in English and held by 1 WorldCat member library worldwide

Mixing time of Markov chains on finite and compact lie groups by Yunjiang Jiang( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

This thesis studies the mixing time of three Markov chains on non-abelian groups. The first is a Metropolis Markov chain on the symmetric groups, initially introduced by Hanlon and Diaconis, and the last two are random walks on the special orthogonal groups, known as Rosenthal's walk and Kac's walk respectively. Using input from representation theory and symmetric function theory, it is shown that cut-off phenomena occur under total variation distance for the Hanlon-Diaconis chain and Rosenthal's walk. For the Kac random walk, a combination of functional-analytic and probabilistic techniques are used to establish the first polynomial order upper bound for its mixing time
The design of optimal uniform filter banks with specified composite response by Amir Dembo( Book )

1 edition published in 1985 in English and held by 1 WorldCat member library worldwide

Late points for random walks in two dimensions by Amir Dembo( Book )

1 edition published in 2003 in English and held by 1 WorldCat member library worldwide

Cover times for Brownian motion and random walks in two dimensions( Book )

1 edition published in 2002 in English and held by 1 WorldCat member library worldwide

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Alternative Names
Amir Dembo American mathematician

Amir Dembo Amerikaans wiskundige

Amir Dembo israelisch-US-amerikanischer Mathematiker

Amir Dembo matematico statunitense

Dembo, A.

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English (116)

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