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

TL;DR

This paper develops the theory of Nash and log-Sobolev inequalities for finite, time-inhomogeneous Markov chains, introducing the concept of c-stability and providing illustrative examples.

Contribution

It extends functional inequalities to the time-inhomogeneous setting and introduces the notion of c-stability for such chains.

Findings

Established basic theory of Nash and log-Sobolev inequalities for inhomogeneous chains

Introduced the concept of c-stability in this context

Provided illustrative examples demonstrating the theory

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.