Random walks and expansion in [formula omitted

Abstract

Let S = { g 1 , … , g k } be a set of elements of SL d ( Z ) generating a Zariski dense subgroup of SL d ( R ) and let p be a sufficiently large prime. Consider the family of Cayley graphs G ( SL d ( Z / p n Z ) , π p n ( S ) ) = G n , where we vary n. Then { G n } forms an expander family. To cite this article: J. Bourgain, A. Gamburd, C. R. Acad. Sci. Paris, Ser. I 346 (2008).