Expansion in finite simple groups of Lie type

By Emmanuel Breuillard, Ben Joseph Green, Robert M. Guralnick, Terence Tao. 2013

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/53a94c5e762fdc2a10bcbc75bde84b4337cfa62b