2005/03/24 by Mark Jerrum, Jung-Bae Son, Prasad Tetali +1 · 1 citation
Mathematics · #math.PR #msc:60J10 #msc:68W20.
paper · pdf · doi:10.1214/105051604000000639
published as Annals of Applied Probability 2004, Vol. 14, No. 4, 1741-1765 · Published 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)
arxiv created 2005/03/24 · arxiv updated 2009/12/01
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.