Large Deviations In Physics PDF Download
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Author | : Angelo Vulpiani |
Publisher | : Springer |
Total Pages | : 323 |
Release | : 2014-05-16 |
Genre | : Science |
ISBN | : 3642542514 |
Download Large Deviations in Physics Book in PDF, ePub and Kindle
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 |
Total Pages | : 372 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1461385334 |
Download Entropy, Large Deviations, and Statistical Mechanics Book in PDF, ePub and Kindle
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 | : Amir Dembo |
Publisher | : Springer Science & Business Media |
Total Pages | : 409 |
Release | : 2009-11-03 |
Genre | : Science |
ISBN | : 3642033113 |
Download Large Deviations Techniques and Applications Book in PDF, ePub and Kindle
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.
Author | : Frank Hollander |
Publisher | : American Mathematical Soc. |
Total Pages | : 164 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780821844359 |
Download Large Deviations Book in PDF, ePub and Kindle
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 | : Daniel W. Stroock |
Publisher | : Springer Science & Business Media |
Total Pages | : 196 |
Release | : 2005-03-30 |
Genre | : Mathematics |
ISBN | : 9783540234517 |
Download An Introduction to Markov Processes Book in PDF, ePub and Kindle
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 | : Richard S. Ellis |
Publisher | : Taylor & Francis |
Total Pages | : 392 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 9783540290599 |
Download Entropy, Large Deviations, and Statistical Mechanics Book in PDF, ePub and Kindle
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 | : R. S. Ellis |
Publisher | : |
Total Pages | : 380 |
Release | : 1985-06-19 |
Genre | : |
ISBN | : 9781461385349 |
Download Entropy, Large Deviations, and Statistical Mechanics Book in PDF, ePub and Kindle
Author | : Jean-Dominique Deuschel |
Publisher | : American Mathematical Soc. |
Total Pages | : 298 |
Release | : 2001 |
Genre | : Large deviations |
ISBN | : 082182757X |
Download Large Deviations Book in PDF, ePub and Kindle
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 | : S. R. S. Varadhan |
Publisher | : SIAM |
Total Pages | : 74 |
Release | : 1984-01-31 |
Genre | : Mathematics |
ISBN | : 0898711894 |
Download Large Deviations and Applications Book in PDF, ePub and Kindle
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 | : Enzo Olivieri |
Publisher | : Cambridge University Press |
Total Pages | : 540 |
Release | : 2005-02-21 |
Genre | : Mathematics |
ISBN | : 9780521591638 |
Download Large Deviations and Metastability Book in PDF, ePub and Kindle
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