Expansion in finite simple groups of Lie type
Emmanuel Breuillard
Université Paris-Sud 11, Orsay, FranceBen J. Green
University of Oxford, United KingdomRobert M. Guralnick
University of Southern California, Los Angeles, United StatesTerence Tao
University of California Los Angeles, United States
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 [BGGT].
Cite this article
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. 1367–1434
DOI 10.4171/JEMS/533