Expansion in SLd(Z/qZ), q arbitrary

• 成果类型: Article
• 署名作者: Bourgain, Jean; Varju, Peter P.
• 署名单位: Institute for Advanced Study - USA; Princeton University; Szeged University; Hungarian Academy of Sciences
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0345-4
• 发表日期: 2012
• 页码: 151-173
• 关键词: random-walks; semigroups; graphs; bounds

摘要

Let S be a fixed finite symmetric subset of SLd(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of pi(q)(G) with respect to the generating set pi(q)(S) form a family of expanders, where pi(q) is the projection map Z -> Z/qZ.