JournalsjemsVol. 10, No. 4pp. 987–1011

Expansion and random walks in SL<em><sub>d</sub></em>(ℤ/<em>p<sup>n</sup></em>ℤ): I

  • Jean Bourgain

    Institute for Advanced Study, Princeton, United States
  • Alex Gamburd

    University of California at Santa Cruz, United States
Expansion and random walks in SL<em><sub>d</sub></em>(ℤ/<em>p<sup>n</sup></em>ℤ): I cover

Abstract

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

Cite this article

Jean Bourgain, Alex Gamburd, Expansion and random walks in SL<em><sub>d</sub></em>(ℤ/<em>p<sup>n</sup></em>ℤ): I. J. Eur. Math. Soc. 10 (2008), no. 4, pp. 987–1011

DOI 10.4171/JEMS/137