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Random Walk Intersections: Large Deviations and Related Topics

Xia Chen University of Tennessee, Knoxville, TN
Available Formats:
Hardcover ISBN: 978-0-8218-4820-3
Product Code: SURV/157
List Price: $101.00 MAA Member Price:$90.90
AMS Member Price: $80.80 Electronic ISBN: 978-1-4704-1384-2 Product Code: SURV/157.E List Price:$95.00
MAA Member Price: $85.50 AMS Member Price:$76.00
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List Price: $151.50 MAA Member Price:$136.35
AMS Member Price: $121.20 Click above image for expanded view Random Walk Intersections: Large Deviations and Related Topics Xia Chen University of Tennessee, Knoxville, TN Available Formats:  Hardcover ISBN: 978-0-8218-4820-3 Product Code: SURV/157  List Price:$101.00 MAA Member Price: $90.90 AMS Member Price:$80.80
 Electronic ISBN: 978-1-4704-1384-2 Product Code: SURV/157.E
 List Price: $95.00 MAA Member Price:$85.50 AMS Member Price: $76.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$151.50 MAA Member Price: $136.35 AMS Member Price:$121.20
• 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.

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

• 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 reviewers who would like to review an AMS book
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.

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 reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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