On laws of large numbers for random walks
2006 (English)In: Annals of Probability, ISSN 0091-1798, Vol. 34, no 5, 1693-1706 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2006. Vol. 34, no 5, 1693-1706 p.
law of large numbers, random walk, multiplicative ergodic theorem, horofunctions, boundary, trees
IdentifiersURN: urn:nbn:se:kth:diva-16172DOI: 10.1214/009117906000000296ISI: 000242464000003ScopusID: 2-s2.0-33845256078OAI: oai:DiVA.org:kth-16172DiVA: diva2:334214
QC 201005252010-08-052010-08-05Bibliographically approved