Merging for inhomogeneous finite Markov chains, part II: Nash and log-Sobolev inequalities

Abstract

We study time-inhomogeneous Markov chains with finite state spaces using Nash and logarithmic-Sobolev inequalities, and the notion of $c$-stability. We develop the basic theory of such functional inequalities in the time-inhomogeneous context and provide illustrating examples.

Published in at http://dx.doi.org/10.1214/10-AOP572 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Quantitative bounds on convergence of time-inhomogeneous Markov chains
• Refined estimates for some basic random walks on the symmetric and alternating groups
• Time inhomogeneous Markov chains with wave-like behavior