Journal of the European Mathematical Society

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Volume 10, Issue 4, 2008, pp. 987–1011
DOI: 10.4171/JEMS/137

Expansion and random walks in SLd(ℤ/pnℤ): I

Jean Bourgain[1] and Alex Gamburd[2]

(1) School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, NJ 08540, PRINCETON, UNITED STATES
(2) Department of Mathematics, University of California at Santa Cruz, 1156 High Street, CA 95064, SANTA CRUZ, UNITED STATES

We prove that Cayley graphs of SLd(ℤ/pnℤ) are expanders with respect to the projection of any fixed elements in SL2(ℤ) generating a Zariski-dense subgroup.

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Bourgain Jean, Gamburd Alex: Expansion and random walks in SLd(ℤ/pnℤ): I. J. Eur. Math. Soc. 10 (2008), 987-1011. doi: 10.4171/JEMS/137