On laws of large numbers for random walks

• 成果类型: Article
• 署名作者: Karlsson, Anders; Ledrappier, Francois
• 署名单位: Royal Institute of Technology; University of Notre Dame
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000296
• 发表日期: 2006
• 页码: 1693-1706
• 关键词: boundary; trees

摘要

We prove a general noncommutative law of large numbers. This applies in particular to random walks on any locally finite homogeneous graph, as well as to Brownian motion on Riemannian manifolds which admit a compact quotient. It also generalizes Oseledec's multiplicative ergodic theorem. In addition, we show that epsilon-shadows of any ballistic random walk with finite moment on any group eventually intersect. Some related results concerning Coxeter groups and mapping class groups are recorded in the last section.