Large Deviations in Physics
Title | Large Deviations in Physics PDF eBook |
Author | Angelo Vulpiani |
Publisher | Springer |
Pages | 323 |
Release | 2014-05-16 |
Genre | Science |
ISBN | 3642542514 |
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
Title | Entropy, Large Deviations, and Statistical Mechanics PDF eBook |
Author | Richard.S. Ellis |
Publisher | Springer Science & Business Media |
Pages | 372 |
Release | 2012-12-06 |
Genre | Science |
ISBN | 1461385334 |
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 Techniques and Applications
Title | Large Deviations Techniques and Applications PDF eBook |
Author | Amir Dembo |
Publisher | Springer Science & Business Media |
Pages | 409 |
Release | 2009-11-03 |
Genre | Science |
ISBN | 3642033113 |
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
Title | Large Deviations PDF eBook |
Author | Frank Hollander |
Publisher | American Mathematical Soc. |
Pages | 164 |
Release | 2000 |
Genre | Mathematics |
ISBN | 9780821844359 |
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.
An Introduction to Markov Processes
Title | An Introduction to Markov Processes PDF eBook |
Author | Daniel W. Stroock |
Publisher | Springer Science & Business Media |
Pages | 196 |
Release | 2005-03-30 |
Genre | Mathematics |
ISBN | 9783540234517 |
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
Entropy, Large Deviations, and Statistical Mechanics
Title | Entropy, Large Deviations, and Statistical Mechanics PDF eBook |
Author | R. S. Ellis |
Publisher | |
Pages | 380 |
Release | 1985-06-19 |
Genre | |
ISBN | 9781461385349 |
Large Deviations
Title | Large Deviations PDF eBook |
Author | Frank Hollander |
Publisher | Amer Mathematical Society |
Pages | 143 |
Release | 2000 |
Genre | Mathematics |
ISBN | 9780821819890 |
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.