Elementary bounds on Poincare and log-Sobolev constants for decomposable Markov chains

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dc.creatorJerrum, Mark
dc.creatorSon, Jung-Bae
dc.creatorTetali, Prasad
dc.creatorVigoda, Eric
dc.date2005-03-24
dc.date.accessioned2026-07-07T05:18:21Z
dc.date.available2026-07-07T05:18:21Z
dc.descriptionWe 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051604000000639 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503537
dc.identifierhttp://arxiv.org/abs/math/0503537
dc.identifierAnnals of Applied Probability 2004, Vol. 14, No. 4, 1741-1765
dc.identifierdoi:10.1214/105051604000000639
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74633
dc.subjectProbability
dc.subject60J10, 68W20. (Primary)
dc.titleElementary bounds on Poincare and log-Sobolev constants for decomposable Markov chains
dc.typetext

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