Random walks and expansion in \(\text{SL}_d(\mathbb{Z}/p^n\mathbb{Z})\).

DOI10.1016/j.crma.2008.04.006zbMath1150.20035OpenAlexW1556156972MaRDI QIDQ931800

Jean Bourgain, Alexander Gamburd

Publication date: 26 June 2008

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.04.006

zbMATH Keywords

Cayley graphsexpander familiesZariski dense subgroups

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Linear algebraic groups over finite fields (20G40) Generators, relations, and presentations of groups (20F05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (2)

Strong approximation in random towers of graphs. ⋮ Arithmetic and dynamics on varieties of Markoff type

Cites Work

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• Affine linear sieve, expanders, and sum-product
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• Bounds for multiplicities of automorphic representations
• Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• Sieving and expanders
• Produits de matrices aléatoires et applications aux propriétés géometriques des sous-groupes du groupe linéaire
• Heegaard genus and property τ for hyperbolic 3-manifolds

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