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Large Deviations
Frank den Hollander, Nijmegen University, Netherlands
A co-publication of the AMS and Fields Institute.
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Fields Institute Monographs
2000; 146 pp; softcover
Volume: 14
ISBN-10: 0-8218-4435-0
ISBN-13: 978-0-8218-4435-9
List Price: US$54
Member Price: US$43.20
Order Code: FIM/14.S
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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 theory its 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.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Advanced graduate students and research mathematicians interested in probability, statistics, ergodic theory, and statistical physics; senior researchers seeking to learn more about statistical physics.

Reviews

"The book is ... a welcome addition ... ideally suited for nonspecialists interested in learning the subject ... One advantage it has over the other books is its brevity ... the appendix, containing solutions to the exercises, is an attractive feature, making the book suitable for self-study ... provides a quick, relatively painless introduction to the subject ... Indeed ... is user-friendly."

-- CMS Notes

"The author has succeeded in presenting the main theorems on large deviations in a clear and readable style, making transparent the role played by the general principles on which the theory is based."

-- Mathematical Reviews

"This is a useful book on large deviations. It can be used as a text for advanced PhD students with a really good background in mathematical analysis and probability theory."

-- European Mathematical Society Newsletter

Table of Contents

Theory
  • Large deviations for i.i.d. sequences: Part 1
  • Large deviations for i.i.d. sequences: Part 2
  • General theory
  • Large deviations for Markov sequences
  • Large deviations for dependent sequences
Applications
  • Statistical hypothesis testing
  • Random walk in random environment
  • Heat conduction with random sources and sinks
  • Polymer chains
  • Interacting diffusions
  • Solutions to the exercises
  • Bibliography
  • Index
  • Glossary of symbols
  • Errata
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