Large Deviations In Physics

Author : Angelo Vulpiani,Fabio Cecconi,Massimo Cencini,Andrea Puglisi,Davide Vergni
Publisher : Springer
Page : 314 pages
File Size : 46,9 Mb
Release : 2014-05-16
Category : Science
ISBN : 9783642542510

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Large Deviations in Physics by Angelo Vulpiani,Fabio Cecconi,Massimo Cencini,Andrea Puglisi,Davide Vergni Pdf

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.

Author : Richard.S. Ellis
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461385332

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Entropy, Large Deviations, and Statistical Mechanics by Richard.S. Ellis Pdf

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.

Author : Frank Hollander
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 55,6 Mb
Release : 2000
Category : Mathematics
ISBN : 0821844350

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Large Deviations by Frank Hollander Pdf

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.

Author : Richard S. Ellis
Publisher : Taylor & Francis
Page : 392 pages
File Size : 49,7 Mb
Release : 2006
Category : Mathematics
ISBN : 3540290591

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Entropy, Large Deviations, and Statistical Mechanics by Richard S. Ellis Pdf

From the reviews: "... Besides the fact that the author's treatment of large deviations is a nice contribution to the literature on the subject, his book has the virue that it provides a beautifully unified and mathematically appealing account of certain aspects of statistical mechanics. ... Furthermore, he does not make the mistake of assuming that his mathematical audience will be familiar with the physics and has done an admireable job of explaining the necessary physical background. Finally, it is clear that the author's book is the product of many painstaking hours of work; and the reviewer is confident that its readers will benefit from his efforts." D. Stroock in Mathematical Reviews 1985 "... Each chapter of the book is followed by a notes section and by a problems section. There are over 100 problems, many of which have hints. The book may be recommended as a text, it provides a completly self-contained reading ..." S. Pogosian in Zentralblatt für Mathematik 1986

Author : Daniel W. Stroock
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 40,9 Mb
Release : 2005-03-30
Category : Mathematics
ISBN : 3540234519

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An Introduction to Markov Processes by Daniel W. Stroock Pdf

Provides a more accessible introduction than other books on Markov processes by emphasizing the structure of the subject and avoiding sophisticated measure theory Leads the reader to a rigorous understanding of basic theory

Author : R. S. Ellis
Publisher : Unknown
Page : 380 pages
File Size : 46,9 Mb
Release : 1985-06-19
Category : Electronic
ISBN : 1461385342

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Entropy, Large Deviations, and Statistical Mechanics by R. S. Ellis Pdf

Author : Frank Hollander
Publisher : Amer Mathematical Society
Page : 143 pages
File Size : 47,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0821819895

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Large Deviations by Frank Hollander Pdf

This volume offers an introduction to large deviations. It is divided into two parts: theory and applications. Basic large deviation theorems are presented for i.i.d. sequences, Markov sequences, and sequences with moderate dependence. The rate function is computed explicitly. The theory is explained without too much emphasis on technicalities. Also included is an outline of general definitions and theorems. The goal is to expose the unified theme that gives large deviation theoryits overall structure, which can be made to work in many concrete cases. The section on applications focuses on recent work in statistical physics and random media.This book contains 60 exercises (with solutions) that should elucidate the content and engage the reader. Prerequisites for the book are a strong background in probability and analysis and some knowledge of statistical physics. It would make an excellent textbook for a special topics course in large deviations.

Author : Richard Durrett
Publisher : American Mathematical Soc.
Page : 380 pages
File Size : 55,9 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821850428

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Particle Systems, Random Media, and Large Deviations by Richard Durrett Pdf

This volume covers the proceedings of the 1984 AMS Summer Research Conference. 'The Mathematics of Phase Transitions' provides a handy summary of results from some of the most exciting areas in probability theory today; interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations. Thirty-seven mathematicians, many of them well-known probabilists, collaborated to produce this readable introduction to the main results and unsolved problems in the field. In fact, it is one of the very few collections of articles yet to be published on these topics. To appreciate many of the articles, an undergraduate course in probability is sufficient. The book will be valuable to probabilists, especially those interested in mathematical physics and to physicists interested in statistical mechanics or disordered systems.

Author : Richard Steven Ellis
Publisher : Unknown
Page : 364 pages
File Size : 43,5 Mb
Release : 1985
Category : Entropie
ISBN : 354096052X

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Entropy, Large Deviations, and Statistical Mechanics by Richard Steven Ellis Pdf

Author : L. Saulis,V.A. Statulevicius
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401135306

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Limit Theorems for Large Deviations by L. Saulis,V.A. Statulevicius Pdf

"Et moi ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O.H ea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service. topology has rendered mathematical physics .. .':: 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1:re of this series

Author : S. R. S. Varadhan
Publisher : SIAM
Page : 80 pages
File Size : 46,8 Mb
Release : 1984-01-01
Category : Mathematics
ISBN : 1611970245

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Large Deviations and Applications by S. R. S. Varadhan Pdf

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.

Author : A.T. Skjeltorp,Tamas Vicsek
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401004190

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Complexity from Microscopic to Macroscopic Scales: Coherence and Large Deviations by A.T. Skjeltorp,Tamas Vicsek Pdf

Many mesoscopic systems display `adaptive' behaviour - changes in some physical property that results from a small change in an internal or external driving force. There is a kind of progression in adaptive phenomena, from quantum mesoscopics to complex, evolved cooperative systems and large scale events like turbulence. The field of mesoscopic magnetism, especially quantum coherence and quantum tunnelling in spin systems, and the coupling between mesoscopic magnetism and mesoscopic transport is currently a very active area of solid state physics. `Dephasing' is an important concept in mesoscopic systems like these. A basic question is the limit at which quantum mechanics breaks down and what it can be replaced with. Another interesting crossover is that between complexity and large excursions or events, with turbulence as a prototype example. The book also contains a discussion of finance. Qualitatively speaking, turbulence and financial markets are apparently similar, so our understanding of turbulence may be relevant to understanding price fluctuations.

Author : Jean-Dominique Deuschel,Daniel W. Stroock
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 54,7 Mb
Release : 2001
Category : Large deviations
ISBN : 9780821827574

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Large Deviations by Jean-Dominique Deuschel,Daniel W. Stroock Pdf

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).

Author : Xia Chen
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 41,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821848203

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Random Walk Intersections by Xia Chen Pdf

Involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry.

Author : Amir Dembo,Ofer Zeitouni
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 52,7 Mb
Release : 2009-11-03
Category : Science
ISBN : 9783642033117

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Large Deviations Techniques and Applications by Amir Dembo,Ofer Zeitouni Pdf

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.