Orthogonality and probability: mixing times

TL;DR

This paper introduces a novel method using orthogonal polynomials to bound the total variation distance and estimate mixing times of discrete reversible Markov chains, enhancing understanding of their convergence behavior.

Contribution

It presents the first application of the Karlin-McGregor approach with orthogonal polynomial diagonalization for analyzing mixing times in Markov chains.

Findings

Bounding total variation distance using orthogonal polynomials

Estimating mixing times via diagonalization techniques

First example demonstrating this approach

Abstract

We produce the first example of bounding total variation distance to stationarity and estimating mixing times via orthogonal polynomials diagonalization of discrete reversible Markov chains, the Karlin-McGregor approach.