Expansion and random walks in $\mathrm{SL}_d(\mathbb{Z}/p^n \mathbb{Z})$: II

Jean Bourgain; Alex Gamburd

doi:10.4171/jems/175

JournalsjemsVol. 11, No. 5pp. 1057–1103

Expansion and random walks in $SL_{d} (Z / p^{n} Z)$ : II

Jean Bourgain
Institute for Advanced Study, Princeton, United States
Alex Gamburd
University of California at Santa Cruz, United States

$Expansion and random walks in $\mathrm{SL}_d(\mathbb{Z}/p^n \mathbb{Z})$: II cover$

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Abstract

We prove that Cayley graphs of $SL_{d} (Z / p^{n} Z)$ are expanders with respect to the projection of any fixed elements in $SL_{d} (Z)$ generating a Zariski dense subgroup.

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Jean Bourgain, Alex Gamburd, Expansion and random walks in $SL_{d} (Z / p^{n} Z)$ : II. J. Eur. Math. Soc. 11 (2009), no. 5, pp. 1057–1103

DOI 10.4171/JEMS/175