Uniform expansion bounds for Cayley graphs of SL2(𝔽p)

2008/03/01 by Jean Bourgain, Alex Gamburd · 264 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Cayley graph #Combinatorics #Discrete mathematics #Finite Group Theory Research #Graph #Mathematics

paper · pdf · doi:10.4007/annals.2008.167.625

published in Annals of Mathematics 167(2), 625-642 (Princeton University)

openalex publication_date 2008/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

We prove that Cayley graphs of SL 2 (F p ) are expanders with respect to the projection of any fixed elements in SL(2, Z) generating a non-elementary subgroup, and with respect to generators chosen at random in SL 2 (F p ).

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• Strong uniform expansion in SL(2,p)
• Expansion, Random Walks and Sieving in SL₂ (\mathbbF_p [t])
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