Entropy, Large Deviations, and Statistical Mechanics

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Taylor & Francis, 2006 - Language Arts & Disciplines - 364 pages

From the reviews:

"... Besides the fact that the author's treatment of large deviations is a nice contribution to the literature on the subject, his book has the virue that it provides a beautifully unified and mathematically appealing account of certain aspects of statistical mechanics. ... Furthermore, he does not make the mistake of assuming that his mathematical audience will be familiar with the physics and has done an admireable job of explaining the necessary physical background. Finally, it is clear that the author's book is the product of many painstaking hours of work; and the reviewer is confident that its readers will benefit from his efforts." D. Stroock in Mathematical Reviews 1985

"... Each chapter of the book is followed by a notes section and by a problems section. There are over 100 problems, many of which have hints. The book may be recommended as a text, it provides a completly self-contained reading ..." S. Pogosian in Zentralblatt für Mathematik 1986

 

Contents

Introduction to Large Deviations
3
8
27
4
33
6
46
9
56
Ferromagnetic Models on Z
88
46
116
55
122
Large Deviations for Random Vectors
229
Level2 Large Deviations for I I D Random Vectors
250
Level3 Large Deviations for I I D Random Vectors
269
Probability
295
Proofs of Two Theorems in Section II 7
319
Existence of the Specific Gibbs Free Energy
332
References
338
Author Index
353

1
138
Convex Functions and the LegendreFenchel Transform
211

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About the author (2006)

Richard S. Ellis received his B.A. degree in mathematics and German literature from Harvard University in 1969 and his Ph.D. degree in mathematics from New York University in 1972. After spending three years at Northwestern University, he moved to the University of Massachusetts, Amherst, where he is a Professor in the Department of Mathematics and Statistics and Adjunct Professor in the Department of Judaic and Near Eastern Studies. His research interests in mathematics focus on the theory of large deviations and on applications to statistical mechanics and other areas. Information on his interests outside mathematics is available at http://www.math.umass.edu/~rsellis. He is Alison’s husband and Melissa’s and Michael’s father.