Entropy, Large Deviations, And Statistical Mechanics

by Ellis, Richard S.

• ISBN13: 9783540290599
• ISBN10: 3540290591
• Format: Paperback
• Copyright: 2006-01-15
• Publisher: Springer Verlag

Summary

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

Author Biography

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.

Table of Contents

Large deviations and statistical mechanics
Introduction to large deviations	p. 3
Large deviation property and asymptotics of integrals	p. 30
Large deviations and the discrete ideal gas	p. 59
Ferromagnetic models on Z	p. 88
Magnetic models on Z[superscript D] and on the circle	p. 138
Convexity and proofs of large deviation theorems
Convex functions and the Legendre-Fenchel transform	p. 211
Large deviations for random vectors	p. 229
Level-2 large deviations for I.I.D. random vectors	p. 250
Level-3 large deviations for I.I.D. random vectors	p. 269
Probability	p. 295
Proofs of two theorems in section II.7	p. 319
Equivalent notions of infinite-volume measures for spin systems	p. 323
Existence of the specific Gibbs free energy	p. 332
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