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Large Deviations
 
Frank den Hollander Nijmegen University, Nijmegen, Netherlands
A co-publication of the AMS and Fields Institute
Large Deviations
Softcover ISBN:  978-0-8218-4435-9
Product Code:  FIM/14.S
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-1-4704-3141-9
Product Code:  FIM/14.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
Softcover ISBN:  978-0-8218-4435-9
eBook: ISBN:  978-1-4704-3141-9
Product Code:  FIM/14.S.B
List Price: $125.00 $95.00
MAA Member Price: $112.50 $85.50
AMS Member Price: $100.00 $76.00
Large Deviations
Click above image for expanded view
Large Deviations
Frank den Hollander Nijmegen University, Nijmegen, Netherlands
A co-publication of the AMS and Fields Institute
Softcover ISBN:  978-0-8218-4435-9
Product Code:  FIM/14.S
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-1-4704-3141-9
Product Code:  FIM/14.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
Softcover ISBN:  978-0-8218-4435-9
eBook ISBN:  978-1-4704-3141-9
Product Code:  FIM/14.S.B
List Price: $125.00 $95.00
MAA Member Price: $112.50 $85.50
AMS Member Price: $100.00 $76.00
  • Book Details
     
     
    Fields Institute Monographs
    Volume: 142000; 143 pp
    MSC: 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.

    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.

  • 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 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 142000; 143 pp
MSC: 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.

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.

  • 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 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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