Softcover ISBN:  9780821844359 
Product Code:  FIM/14.S 
List Price:  $61.00 
MAA Member Price:  $54.90 
AMS Member Price:  $48.80 
Electronic ISBN:  9781470431419 
Product Code:  FIM/14.E 
List Price:  $57.00 
MAA Member Price:  $51.30 
AMS Member Price:  $45.60 

Book DetailsFields Institute MonographsVolume: 14; 2000; 143 ppMSC: Primary 60; Secondary 82;
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.ReadershipAdvanced graduate students and research mathematicians interested in probability, statistics, ergodic theory, and statistical physics; senior researchers seeking to learn more about statistical physics.

Table of Contents

Part A. Theory

Chapter I. Large deviations for i.i.d. sequences: Part 1

Chapter II. Large deviations for i.i.d. sequences: Part 2

Chapter III. General theory

Chapter IV. Large deviations for Markov sequences

Chapter V. Large deviations for dependent sequences

Part B. Applications

Chapter VI. Statistical hypothesis testing

Chapter VII. Random walk in random environment

Chapter VIII. Heat conduction with random sources and sinks

Chapter IX. Polymer chains

Chapter X. Interacting diffusions

Appendix. Solutions to the exercises


Additional Material

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 selfstudy … provides a quick, relatively painless introduction to the subject … Indeed … is userfriendly.
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


RequestsReview Copy – for reviewers who would like to review an AMS bookAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
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.
Advanced graduate students and research mathematicians interested in probability, statistics, ergodic theory, and statistical physics; senior researchers seeking to learn more about statistical physics.

Part A. Theory

Chapter I. Large deviations for i.i.d. sequences: Part 1

Chapter II. Large deviations for i.i.d. sequences: Part 2

Chapter III. General theory

Chapter IV. Large deviations for Markov sequences

Chapter V. Large deviations for dependent sequences

Part B. Applications

Chapter VI. Statistical hypothesis testing

Chapter VII. Random walk in random environment

Chapter VIII. Heat conduction with random sources and sinks

Chapter IX. Polymer chains

Chapter X. Interacting diffusions

Appendix. Solutions to the exercises

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 selfstudy … provides a quick, relatively painless introduction to the subject … Indeed … is userfriendly.
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