**Courant Lecture Notes**

Volume: 27;
2016;
104 pp;
Softcover

MSC: Primary 60;

**Print ISBN: 978-0-8218-4086-3
Product Code: CLN/27**

List Price: $36.00

AMS Member Price: $28.80

MAA Member Price: $32.40

**Electronic ISBN: 978-1-4704-3585-1
Product Code: CLN/27.E**

List Price: $36.00

AMS Member Price: $28.80

MAA Member Price: $32.40

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#### Supplemental Materials

# Large Deviations

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*S. R. S. Varadhan*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

The theory of large deviations deals with
rates at which probabilities of certain events decay as a natural
parameter in the problem varies. This book, which is based on a
graduate course on large deviations at the Courant Institute, focuses
on three concrete sets of examples: (i) diffusions with small noise
and the exit problem, (ii) large time behavior of Markov processes and
their connection to the Feynman-Kac formula and the related large
deviation behavior of the number of distinct sites visited by a random
walk, and (iii) interacting particle systems, their scaling limits,
and large deviations from their expected limits. For the most part the
examples are worked out in detail, and in the process the subject of
large deviations is developed.

The book will give the reader a flavor of how large deviation
theory can help in problems that are not posed directly in terms of
large deviations. The reader is assumed to have some familiarity with
probability, Markov processes, and interacting particle systems.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

#### Readership

Graduate students and researchers interested in large deviations.

#### Reviews & Endorsements

This book is a good source for advanced graduate students and researchers who wish to learn how large deviations appear in questions of probability and statistical physics that are not directly formulated in such terms, as well as several techniques for proving LDPs in concrete situations.

-- Max Fathi, Mathematical Reviews

#### Table of Contents

# Table of Contents

## Large Deviations

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Chapter 1. Introduction 110
- Chapter 2. Basic Formulation 514
- Chapter 3. Small Noise 1322
- Chapter 4. Large Time 2938
- Chapter 5. Hydrodynamic Scaling 4554
- Chapter 6. Self-Diffusion 7180
- Chapter 7. Nongradient Systems 7988
- Chapter 8. Some Comments About TASEP 99108
- Bibliography 103112
- Back Cover Back Cover1114