Strong uniform expansion in \(\text{SL}(2,p)\).

DOI10.1007/s00039-010-0094-3zbMath1253.20051arXiv0911.3022OpenAlexW2019994888MaRDI QIDQ607667

Alexander Gamburd, Emmanuel Breuillard

Publication date: 3 December 2010

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.3022

zbMATH Keywords

finite groupsrandom walksCayley graphsgenerating setsTits alternativespecial linear groupsexpander graphs

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Probability theory on algebraic and topological structures (60B99) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

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Cites Work

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• Expansion of product replacement graphs
• Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators
• Finite groups of uniform logarithmic diameter.
• Fields of large transcendence degree generated by values of elliptic functions
• Ramanujan graphs
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• Entropy waves, the zig-zag graph product, and new constant-degree expanders
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• Symmetric groups and expander graphs.
• Symmetric Random Walks on Groups
• Expander graphs and their applications
• Generating random elements of a finite group
• On the difference between consecutive primes