Let 1 be a non-trivial group word, let be a finite simple group, and let be the set of values of in . We show that if is large, then the random walk on with respect to as a generating set has mixing time 2.
This strengthens various known results, for example the fact that covers almost all of .
Cite this article
Gili Schul, Aner Shalev, Words and mixing times in finite simple groups. Groups Geom. Dyn. 5 (2011), no. 2, pp. 509–527DOI 10.4171/GGD/137