On laws of large numbers for random walks

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 $\epsilon$-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.

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)

References in corpus (1)

• Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry

Cited by in corpus (8)

• Asymptotic entropy and green speed for random walks on countable groups
• Sublinear deviation between geodesics and sample paths
• Notes on the Multiplicative Ergodic Theorem
• The horofunction boundary of a Gromov hyperbolic space
• Two extensions of Thurston's spectral theorem for surface diffeomorphisms
• The asymptotic shape theorem for generalized first passage percolation
• Random walks and contracting elements I: Deviation inequality and Limit laws
• Finite Voronoi decompositions of infinite vertex transitive graphs