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Random Walk Intersections: Large Deviations and Related Topics
 
Xia Chen University of Tennessee, Knoxville, TN
Random Walk Intersections
Hardcover ISBN:  978-0-8218-4820-3
Product Code:  SURV/157
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1384-2
Product Code:  SURV/157.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4820-3
eBook: ISBN:  978-1-4704-1384-2
Product Code:  SURV/157.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Random Walk Intersections
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Random Walk Intersections: Large Deviations and Related Topics
Xia Chen University of Tennessee, Knoxville, TN
Hardcover ISBN:  978-0-8218-4820-3
Product Code:  SURV/157
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1384-2
Product Code:  SURV/157.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4820-3
eBook ISBN:  978-1-4704-1384-2
Product Code:  SURV/157.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1572010; 332 pp
    MSC: Primary 60; 81; 82;

    The material covered in this book involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry. The development carefully provides the basic definitions of mutual intersection and self-intersection local times for Brownian motions and the accompanying large deviation results. The book then proceeds to the analogues of these concepts and results for random walks on lattices of \(R^d\). This includes suitable integrability and large deviation results for these models and some applications. Moreover, the notes and comments at the end of the chapters provide interesting remarks and references to various related results, as well as a good number of exercises. The author provides a beautiful development of these subtle topics at a level accessible to advanced graduate students.

    Readership

    Graduate students and research mathematicians interested in probability and statistical physics.

  • Table of Contents
     
     
    • Chapters
    • 1. Basics on large deviations
    • 2. Brownian intersection local times
    • 3. Mutual intersection: large deviations
    • 4. Self-intersection: large deviations
    • 5. Intersections on lattices: weak convergence
    • 6. Inequalities and integrabilities
    • 7. Independent random walks: large deviations
    • 8. Single random walk: large deviations
    • Appendix
  • Reviews
     
     
    • [T]he author is a leading expert who has made crucial contributions. ...This book covers a fascinating topic of current interest, collecting in one place and in a systematic way results that are scattered in the literature. Chen attempts to make the text essentially self-contained, and develops along the way the necessary tools. The book can be rather demanding in places but the motivated reader will draw many benefits from following the development.

      Ofer Zeitouni, Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1572010; 332 pp
MSC: Primary 60; 81; 82;

The material covered in this book involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry. The development carefully provides the basic definitions of mutual intersection and self-intersection local times for Brownian motions and the accompanying large deviation results. The book then proceeds to the analogues of these concepts and results for random walks on lattices of \(R^d\). This includes suitable integrability and large deviation results for these models and some applications. Moreover, the notes and comments at the end of the chapters provide interesting remarks and references to various related results, as well as a good number of exercises. The author provides a beautiful development of these subtle topics at a level accessible to advanced graduate students.

Readership

Graduate students and research mathematicians interested in probability and statistical physics.

  • Chapters
  • 1. Basics on large deviations
  • 2. Brownian intersection local times
  • 3. Mutual intersection: large deviations
  • 4. Self-intersection: large deviations
  • 5. Intersections on lattices: weak convergence
  • 6. Inequalities and integrabilities
  • 7. Independent random walks: large deviations
  • 8. Single random walk: large deviations
  • Appendix
  • [T]he author is a leading expert who has made crucial contributions. ...This book covers a fascinating topic of current interest, collecting in one place and in a systematic way results that are scattered in the literature. Chen attempts to make the text essentially self-contained, and develops along the way the necessary tools. The book can be rather demanding in places but the motivated reader will draw many benefits from following the development.

    Ofer Zeitouni, Mathematical Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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