On laws of large numbers for random walks

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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.
Published at http://dx.doi.org/10.1214/009117906000000296 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Probability, 60F99, 60B99, 37A30 (Primary) 60J50, 60J65 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/119354

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611607
 http://arxiv.org/abs/math/0611607
 Annals of Probability 2006, Vol. 34, No. 5, 1693-1706
 doi:10.1214/009117906000000296

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arXiv