Large Deviations (Fields Institute Monographs) by Frank den Hollander (PDF)

Description

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).

User’s Reviews

Editorial Reviews: Review “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

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If you have relatively solid background on Probability theory but new to large deviation. I would like to recommend this book rather than “Large Deviations Techniques and Applications”. Reasons are follow:1. This book is short. If you don’t care about the application very much, the core content is less than 70 pages. In other words, I recommend to read this book carefully and slowly even over and over, in order to absorb it well. In any case, it is easier to go through “Large Deviations Techniques and Applications”2. Comparing “Large Deviations Techniques and Applications”, I like the presentation, which is very intuitive. The book didn’t prove the very general and very deep results. However, with weaker assumption and much nicer and conciser proof, it will not be difficult to understanding the deeper and harder one.

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