Strong stationary times for features of random walks

TL;DR

This paper explores the use of strong stationary times to analyze the mixing times of statistics on Markov chains, providing a different approach from coupling and examining various behaviors through examples.

Contribution

It introduces the application of strong stationary times to bound mixing times of Markov chain statistics, expanding on previous coupling-based methods.

Findings

Different behaviors in strong stationary times are identified.

Examples illustrate the effectiveness of the approach.

The method offers alternative bounds on mixing times.

Abstract

In [4], we examined the use of coupling to obtain bounds on the mixing time of statistics on Markov chains. In the present paper, we consider the same general problem, but using strong stationary times rather than coupling. We discuss various types of behaviour that may occur when this is attempted, and analyse a variety of examples.