Journal of the European Mathematical Society
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Expansion and random walks in SLd(ℤ/pnℤ): IIJean Bourgain and Alex Gamburd (1) School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, NJ 08540, Princeton, USA
(2) Department of Mathematics, University of California at Santa Cruz, 1156 High Street, CA 95064, Santa Cruz, USA
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): II. J. Eur. Math. Soc. 11 (2009), 1057-1103. doi: 10.4171/JEMS/175