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) Institute for Advanced Study, Princeton, United States
(2) University of California at 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