Choquet-Deny groups and the infinite conjugacy class property

• 成果类型: Article
• 署名作者: Frisch, Joshua; Hartman, Yair; Tamuz, Omer; Ferdowsi, Pooya Vahidi
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2019.190.1.5
• 发表日期: 2019
• 页码: 307-320
• 关键词: random-walks; BOUNDARY; number

摘要

A countable discrete group G is called Choquet-Deny if for every non-degenerate probability measure mu on G, it holds that all bounded mu-harmonic functions are constant. We show that a finitely generated group G is Choquet-Deny if and only if it is virtually nilpotent. For general countable discrete groups, we show that G is Choquet-Deny if and only if none of its quotients has the infinite conjugacy class property. Moreover, when G is not Choquet-Deny, then this is witnessed by a symmetric, finite entropy, non-degenerate measure.