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

Expansion and random walks in SL<em><sub>d</sub></em>(ℤ/<em>p<sup>n</sup></em>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 SL<em><sub>d</sub></em>(ℤ/<em>p<sup>n</sup></em>ℤ): II cover
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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): II. J. Eur. Math. Soc. 11 (2009), no. 5, pp. 1057–1103

DOI 10.4171/JEMS/175