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 [BGGT].
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Emmanuel Breuillard, Ben J. Green, Robert M. Guralnick, Terence Tao, Expansion in finite simple groups of Lie type. J. Eur. Math. Soc. 17 (2015), no. 6, pp. 1367–1434DOI 10.4171/JEMS/533