Random walks on the affine group of local fields and of homogeneous trees

DOI10.5802/aif.1433zbMath0809.60010OpenAlexW2025225622MaRDI QIDQ1341654

Wolfgang Woess, Vadim A. Kaimanovich, Donald I. Cartwright

Publication date: 8 January 1995

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1994__44_4_1243_0

zbMATH Keywords

Dirichlet problemrandom walkslaw of large numberscentral limit theoremPoisson boundaryharmonic functionsasymptotic properties of random productsgeometric properties of homogeneous trees

Mathematics Subject Classification ID

Trees (05C05) Sums of independent random variables; random walks (60G50) Harmonic analysis on homogeneous spaces (43A85) Discrete potential theory (31C20) Analysis on (p)-adic Lie groups (22E35) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items

Shannon's theorem for locally compact groups, Boundary and entropy of space homogeneous Markov chains, Random walks on Baumslag-Solitar groups, Recurrence and ergodicity of random walks on linear groups and on homogeneous spaces, Shalom's property \(H_{\mathrm{FD}}\) and extensions by \(\mathbb{Z}\) of locally finite groups, The Martin boundary for harmonic functions on groups of automorphisms of a homogeneous tree, On laws of large numbers for random walks, Poisson boundary for finitely generated groups of rational affinities, Rate of escape on the lamplighter tree, Transition operators on co-compact \(G\)-spaces, Brownian motion on treebolic space: escape to infinity, Boundaries of dense subgroups of totally disconnected groups, Random walks on the affine group of a homogeneous tree in the drift-free case, Poisson representation and Furstenberg entropy of hypergroups, On the invariant measure of the random difference equation \(X_{n} = a_{n}x_{n - 1} + b_{n}\) in the critical case, Factors from trees, Speed of stochastic locally contractive systems., Horocyclic products of trees, Invariance, quasi-invariance, and unimodularity for random graphs, Brownian motion on treebolic space: positive harmonic functions, Poisson boundary of \(GL_d (\mathbb Q)\), The Poisson boundary of random rational affinities, Renewal theory on the affine group of an oriented tree, Rate of escape of random walks on free products, Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs, Random walks on Diestel-Leader graphs, Matsumoto–Yor Process and Infinite Dimensional Hyperbolic Space, Poisson boundary of triangular matrices in a number field, Regular sequences and random walks in affine buildings, Random walks on the discrete affine group

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