Log-Sobolev and Nash Inequalities for Discrete-Time Finite Markov Chains

Yan-Hong Song

2015, v.21, Issue 1, 127-144

ABSTRACT

In the paper, the probability and the generalized Cheeger's method are used
to study the log-Sobolev and Nash inequalities for discrete-time finite
Markov chains. Thus, the quantitative estimates of hypercontractivity
and algebraic convergence for transition matrices are obtained.

Keywords: Markov chains, Log-Sobolev inequality, Nash inequality, hypercontractivity, algebraic convergence