Open Access
September 2006 On laws of large numbers for random walks
Anders Karlsson, François Ledrappier
Ann. Probab. 34(5): 1693-1706 (September 2006). DOI: 10.1214/009117906000000296


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 ɛ-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.


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Anders Karlsson. François Ledrappier. "On laws of large numbers for random walks." Ann. Probab. 34 (5) 1693 - 1706, September 2006.


Published: September 2006
First available in Project Euclid: 14 November 2006

zbMATH: 1111.60005
MathSciNet: MR2271477
Digital Object Identifier: 10.1214/009117906000000296

Primary: 37A30 , 60B99 , 60F99
Secondary: 60J50 , 60J65

Keywords: horofunctions , Law of Large Numbers , multiplicative ergodic theorem , Random walk

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 5 • September 2006
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