Tensor product Markov chains and Weil representations

TL;DR

This paper establishes precise bounds on how quickly certain Markov chains, defined on irreducible representations of finite classical groups via tensoring with Weil representations, converge to their stationary distribution.

Contribution

It provides sharp convergence bounds for Markov chains on irreducible representations of classical groups using Weil representations, extending understanding of their mixing times.

Findings

Sharp bounds on convergence rates established

Applicable to finite general linear, unitary, and symplectic groups

Results improve previous estimates on mixing times

Abstract

We obtain sharp bounds on the convergence rate of Markov chains on irreducible representations of finite general linear, unitary, and symplectic groups (in both odd and even characteristic) given by tensoring with Weil representations.