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On the mean distance of random walks on groups
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Soit G un groupe continu et μ une probabilite a support compact de densite par rapport a la mesure de Haar as discussed by the authors, soient X 1, X 2, … une marche aleatoire sur G associee a μ.Abstract:
Soit G un groupe continu et μ une probabilite a support compact de densite par rapport a la mesure de Haar. Soient X 1 , X 2 , … une marche aleatoire sur G associee a μ. On demontre que chaque fonction harmonique bornee est constante si et seulement si (1/n)|X n |→0 quand n→∞read more
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Linear Drift and Poisson Boundary for Random Walks
TL;DR: In this paper, a non-degenerate random walk on a locally compact group with finite first moment is considered, and it is shown that if there are no nonconstant bounded harmonic functions, all the linear drift comes from a real additive character on the group.
Book ChapterDOI
Ergodic Theory of ℤ d Actions: Boundaries of invariant Markov Operators: The identification problem
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A Lower Estimate for Central Probabilities on Polycyclic Groups
TL;DR: In this article, a lower bound for the central value of the nth convolution power of a symmetric probability measure on a polycyclic group G of exponential growth whose suppose is finite and generates G is given.
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Noncommutative ergodic theorems
TL;DR: In this paper, the asymptotic behavior of ergodic products of isometries of a metric space X has been studied for non-integrable functions, such as random walks on groups and Brownian motion on covering manifolds.
Ergodic theorems for noncommuting random products
TL;DR: In this paper, Navas et al. presented a series of lectures on Probabilistic and Dynamical Properties of Semi-Group Actions at the 2008 Transfer of Knowledge Workshop at the Universidad de Santiago de Chile, Chile.