Expansion in finite simple groups of Lie type

  • Emmanuel Breuillard

    Université Paris-Sud 11, Orsay, France
  • Ben J. Green

    University of Oxford, United Kingdom
  • Robert M. Guralnick

    University of Southern California, Los Angeles, United States
  • Terence Tao

    University of California Los Angeles, United States


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