Semiclassical Analysis, Witten Laplacians, and Statistical Mechanics

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World Scientific, 01.01.2002 - 179 Seiten
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This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log -- Sobolev inequality.
 

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Inhalt

Introduction
1
Witten Laplacians approach
9
Problems in statistical mechanics with
23
Laplace integrals and transfer operators
31
Semiclassical analysis for the transfer
51
Basic facts in spectral theory and on
77
LogSobolev inequalities
101
Uniform decay of correlations
133
Uniform logSobolev inequalities
151
Bibliography
169
Index
177
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Über den Autor (2002)

Bernard Helffer is a Professor in the Department of Mathematics at Universite Paris-Sud. He has published more than 200 papers in mathematics and mathematical physics and authored five books. In 2011 he was awarded the Prix de l'Etat by the French Academy of Sciences.

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