Entropy, Large Deviations, and Statistical Mechanics

Richard S. Ellis

ISBN 10: 038796052X / ISBN 13: 9780387960524

Published by Springer-Verlag, New York, NY, 1985

About this Item

Near Fine: The Book shows mild shelving wear to the lower extremities and even milder wear to the upper corner tips; sun-blanching to the yellow background field of the rear panel (the black titles thereon remain bold and clearly legible) ; the binding is square and secure; the text is clean. Free of creased or dog-eared pages in the text. Free of any underlining, hi-lighting or marginalia or marks in the text. Free of ownership names, dates, addresses, notations, inscriptions, stamps, or labels. A handsome copy, structurally sound and tightly bound, showing mild wear and a single cosmetic imperfection. No DJ as issued. NOT a Remainder, Book-Club, or Ex-Library. Large 8vo (9.5 x 6.35 x 0.9 inches). Language: English. Weight: 25 ounces. Hardcover: No DJ as issued. This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. We will treat a large class of stochastic systems which involve both indepen dent and dependent random variables and which have the following features: probabilities converge to zero exponentially fast as the size of the system increases; the exponential decay leads to strong convergence properties of the system. The most fascinating aspect of the theory is that the exponential decay rates are computable in terms of entropy functions. ; Grundlehren Der Mathematischen Wissenschaften: a Series of Comprehensive Studies in Mathematics; Vol. 271; Large 8vo 9" - 10" tall; xiv, 364 pages.

Seller Inventory # 59381

Bibliographic Details

• Title: Entropy, Large Deviations, and Statistical Mechanics
• Publisher: Springer-Verlag, New York, NY
• Publication Date: 1985
• Language: English
• ISBN 10: 038796052X
• ISBN 13: 9780387960524
• Binding: Hardcover
• Edition: First Edition; First Printing.
• Condition: Near Fine
• Dust Jacket Condition: No Dust Jacket As Issued

About this title

Synopsis

This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. An elementary example is the weak law of large numbers. For each positive e, P{ISn/nl 2: e} con­ verges to zero as n --+ 00, where Sn is the nth partial sum of indepen­ dent identically distributed random variables with zero mean. Large deviation theory shows that if the random variables are exponentially bounded, then the probabilities converge to zero exponentially fast as n --+ 00. The exponen­ tial decay allows one to prove the stronger property of almost sure conver­ gence (Sn/n --+ 0 a.s.). This example will be generalized extensively in the book. We will treat a large class of stochastic systems which involve both indepen­ dent and dependent random variables and which have the following features: probabilities converge to zero exponentially fast as the size of the system increases; the exponential decay leads to strong convergence properties of the system. The most fascinating aspect of the theory is that the exponential decay rates are computable in terms of entropy functions. This identification between entropy and decay rates of large deviation probabilities enhances the theory significantly.

About the Author

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.