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Title:Elementary bounds on Poincar and log-Sobolev constants for decomposable Markov chains
Authors: Mark Jerrum ; Jung-Bae Son ; Prasad Tetali ; Eric Vigoda
Date: 2004
Publication Title:Annals of Applied Probability
Publisher:The Institute of Mathematical Statistics
Publication Type:Journal Article Publication Status:Published
Volume No:14(4) Page Nos:1741-1765
We consider finite-state Markov chains that can be naturally decomposed into smaller ``projection'' and ``restriction'' chains. Possibly this decomposition will be inductive, in that the restriction chains will be smaller copies of the initial chain. We provide expressions for Poincare (resp. log-Sobolev) constants of the initial Markov chain in terms of Poincare (resp. log-Sobolev) constants of the projection and restriction chains, together with further a parameter. In the case of the Poincare constant, our bound is always at least as good as existing ones and, depending on the value of the extra parameter, may be much better. There appears to be no previously published decomposition result for the log-Sobolev constant. Our proofs are elementary and self-contained.
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Bibtex format
author = { Mark Jerrum and Jung-Bae Son and Prasad Tetali and Eric Vigoda },
title = {Elementary bounds on Poincar and log-Sobolev constants for decomposable Markov chains},
journal = {Annals of Applied Probability},
publisher = {The Institute of Mathematical Statistics},
year = 2004,
volume = {14(4)},
pages = {1741-1765},
doi = {10.1214/105051604000000639},
url = {},

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