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On laws of large numbers for random walks

Anders Karlsson·François Ledrappier
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Abstract

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 $ε$-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. 2006-11-20. On laws of large numbers for random walks. https://doi.org/10.1214/009117906000000296

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