Large Deviations And Applications
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Large Deviations And Applications
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Author : S. R. S. Varadhan
language : en
Publisher: SIAM
Release Date : 1984-01-01
Large Deviations And Applications written by S. R. S. Varadhan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.
Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
Large Deviations Techniques And Applications
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Author : Amir Dembo
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-03
Large Deviations Techniques And Applications written by Amir Dembo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-03 with Science categories.
Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate students. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences. The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applications were sharpened, new exercises added, and the bibliography updated. The present soft cover edition is a corrected printing of the 1998 edition.
Large Deviations
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Author : Frank Hollander
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Large Deviations written by Frank Hollander and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.
Large Deviations And Applications The Finite Dimensional Case
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Author :
language : en
Publisher:
Release Date : 1991
Large Deviations And Applications The Finite Dimensional Case written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
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.
Large Deviations
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Author : Frank den Hollander
language : en
Publisher:
Release Date : 2008
Large Deviations written by Frank den Hollander and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
This book is an introduction to the theory and applications of large deviations, a branch of probability theory that describes the probability of rare events in terms of variational problems. By focusing the theory, in Part A of the book, on random sequences, the author succeeds in conveying the main ideas behind large deviations without a need for technicalities, thus providing a concise and accessible entry to this challenging and captivating subject. The selection of modern applications, described in Part B of the book, offers a good sample of what large deviation theory is able to achieve.
Large Deviations And Idempotent Probability
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Author : Anatolii Puhalskii
language : en
Publisher: CRC Press
Release Date : 2001-05-07
Large Deviations And Idempotent Probability written by Anatolii Puhalskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-07 with Business & Economics categories.
In the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak
Large Deviations
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Author : Jean-Dominique Deuschel
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Large Deviations written by Jean-Dominique Deuschel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Large deviations categories.
This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).
Large Deviations In Physics
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Author : Angelo Vulpiani
language : en
Publisher: Springer
Release Date : 2014-05-16
Large Deviations In Physics written by Angelo Vulpiani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-16 with Science categories.
This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.
Entropy Large Deviations And Statistical Mechanics
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Author : Richard.S. Ellis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Entropy Large Deviations And Statistical Mechanics written by Richard.S. Ellis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. An elementary example is the weak law of large numbers. For each positive e, P{ISn/nl 2: e} con verges to zero as n --+ 00, where Sn is the nth partial sum of indepen dent identically distributed random variables with zero mean. Large deviation theory shows that if the random variables are exponentially bounded, then the probabilities converge to zero exponentially fast as n --+ 00. The exponen tial decay allows one to prove the stronger property of almost sure conver gence (Sn/n --+ 0 a.s.). This example will be generalized extensively in the book. We will treat a large class of stochastic systems which involve both indepen dent and dependent random variables and which have the following features: probabilities converge to zero exponentially fast as the size of the system increases; the exponential decay leads to strong convergence properties of the system. The most fascinating aspect of the theory is that the exponential decay rates are computable in terms of entropy functions. This identification between entropy and decay rates of large deviation probabilities enhances the theory significantly.
Large Deviations For Random Graphs
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Author : Sourav Chatterjee
language : en
Publisher: Springer
Release Date : 2017-08-31
Large Deviations For Random Graphs written by Sourav Chatterjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-31 with Mathematics categories.
This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics.