Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
A semidefinite bound for mixing rates of Markov chains
Proceedings of the workshop on Randomized algorithms and computation
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This paper is concerned with path techniques for quantitativeanalysis of the logarithmic Sobolev constant on a countable set. Wepresent new upper bounds on the logarithmic Sobolev constant, whichgeneralize those given by Sinclair [20], in the case of thespectral gap constant involving path combinatorics. Some examplesof applications are given. Then, we compare our bounds to the Hardyconstant in the particular case of birth and death processes.Finally, following the approach of Rosenthal in [18], we generalizeour bounds to continuous sets.