RANDOM WALKS AND ISOPERIMETRIC PROFILES UNDER MOMENT CONDITIONS

• 成果类型: Article
• 署名作者: Saloff-Coste, Laurent; Zheng, Tianyi
• 署名单位: Cornell University; Stanford University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1070
• 发表日期: 2016
• 页码: 4133-4183
• 关键词: markov-chains; Lower bounds; inequalities; entropy; driven; nash

摘要

Let G be a finitely generated group equipped with a finite symmetric generating set and the associated word length function vertical bar center dot vertical bar. We study the behavior of the probability of return for random walks driven by symmetric measures cc that are such that Sigma rho (vertical bar x vertical bar mu(x) < infinity for increasing regularly varying or slowly varying functions rho, for instance, s vertical bar -> (1 + s)(alpha), alpha is an element of(0, 2], or s vertical bar -> (1 + log(1 + s))(epsilon), epsilon > 0. For this purpose, we develop new relations between the isoperimetric profiles associated with different symmetric probability measures. These techniques allow us to obtain a sharp L-2-version of Erschler's inequality concerning the FOlner functions of wreath products. Examples and assorted applications are included.