Comptes Rendus
Group Theory
Random walks and expansion in SLd(Z/pnZ)
Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 619-623.

Let S={g1,,gk} be a set of elements of SLd(Z) generating a Zariski dense subgroup of SLd(R) and let p be a sufficiently large prime. Consider the family of Cayley graphs G(SLd(Z/pnZ),πpn(S))=Gn, where we vary n. Then {Gn} forms an expander family.

Soit S={g1,,gk} un sous-ensemble de SLd(Z) engendrant un sous-groupe de SLd(R) Zariski dense. On considère les graphes de Cayley G(SLd(Z/pnZ),πpn(S))=Gn, òu l'on varie n. Alors {Gn} forment une famille d'expanseurs.

Accepted:
Published online:
DOI: 10.1016/j.crma.2008.04.006

Jean Bourgain 1; Alex Gamburd 1

1 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA
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Jean Bourgain; Alex Gamburd. Random walks and expansion in $ {\mathrm{SL}}_{d}(\mathbb{Z}/{p}^{n}\mathbb{Z})$. Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 619-623. doi : 10.1016/j.crma.2008.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.04.006/

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