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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, 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
URN: urn:nbn:se:kth:diva-16172DOI: 10.1214/009117906000000296ISI: 000242464000003ScopusID: 2-s2.0-33845256078OAI: diva2:334214
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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