Contracting isometries and differentiability of the escape rate

• 成果类型: Article; Early Access
• 署名作者: Choi, Inhyeok
• 署名单位: Korea Institute for Advanced Study (KIAS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01434-0
• 发表日期: 2025
• 关键词: rank-one isometries; random-walks; entropy; geodesics; BOUNDARY; HYPERBOLICITY; geometry; trees; drift

摘要

Let G be a countable group whose action on a metric space X involves a contracting isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces, Teichm & uuml;ller space, Culler-Vogtmann Outer space and CAT(0) spaces. We discuss continuity and differentiability of the escape rate of random walks on G. For relatively hyperbolic groups, CAT(-1) groups and CAT(0) cubical groups, we further discuss analyticity of the escape rate. Finally, assuming that the action of G on X is weakly properly discontinuous (WPD), we discuss continuity of the asymptotic entropy of random walks on G.