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On laws of large numbers for random walks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2006 (English)In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 34, no 5, 1693-1706 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
law of large numbers, random walk, multiplicative ergodic theorem, horofunctions, boundary, trees
Identifiers
URN: urn:nbn:se:kth:diva-16172DOI: 10.1214/009117906000000296ISI: 000242464000003Scopus ID: 2-s2.0-33845256078OAI: oai:DiVA.org:kth-16172DiVA: diva2:334214
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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