Large Deviations

By: S.R.S. Varadhan

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Paperback | 30 December 2016

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Paperback
104 Pages

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18 x 25.4 x 0.9

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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.

Industry Reviews

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

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