Expansion in finite simple groups of Lie type

Abstract

We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper, establishing strongly dense subgroups in simple algebraic groups.

78 pages, 2 figures. This is the final version, incorporating referee comments