Words and mixing times in finite simple groups

Abstract

Let $w\ne$ 1 be a non-trivial group word, let $G$ be a finite simple group, and let $w(G)$ be the set of values of $w$ in $G$. We show that if $G$ is large, then the random walk on $G$ with respect to $w(G)$ as a generating set has mixing time 2.

This strengthens various known results, for example the fact that $w(G{)}^2$ covers almost all of $G$.