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A Path Method for the Logarithmic Sobolev Constant

Published online by Cambridge University Press:  04 July 2003

CYRIL ROBERTO
CYRIL ROBERTO
Affiliation:
Université Paul Sabatier, L.S.P., 118 route de Narbonnes, 31062 Toulouse, France (e-mail: roberto@cict.fr)
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Abstract

This paper is concerned with path techniques for quantitative analysis of the logarithmic Sobolev constant on a countable set. We present new upper bounds on the logarithmic Sobolev constant, which generalize those given by Sinclair [20], in the case of the spectral gap constant involving path combinatorics. Some examples of applications are given. Then, we compare our bounds to the Hardy constant in the particular case of birth and death processes. Finally, following the approach of Rosenthal in [18], we generalize our bounds to continuous sets.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 12 , Issue 4 , July 2003 , pp. 431 - 455
Copyright
2003 Cambridge University Press

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