Poisson boundaries of lamplighter groups: proof of the Kaimanovich-Vershik conjecture

DOI10.4171/JEMS/1030WikidataQ123217712 ScholiaQ123217712MaRDI QIDQ2031664

Yuval Peres, Russell Lyons

Publication date: 10 June 2021

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.01845

zbMATH Keywords

entropyrandom walksharmonic functionsfree metabelian group

Mathematics Subject Classification ID

Geometric group theory (20F65) Measures on groups and semigroups, etc. (43A05) Asymptotic properties of groups (20F69) Boundary theory for Markov processes (60J50) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (8)

Law of large numbers for the drift of the two-dimensional wreath product ⋮ Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters ⋮ Quantitative measure equivalence between amenable groups ⋮ Most transient random walks have infinitely many cut times ⋮ Arboreal structures on groups and the associated boundaries ⋮ Poisson representation and Furstenberg entropy of hypergroups ⋮ Asymptotic behaviors of random walks on countable groups ⋮ Random walks on the discrete affine group

Cites Work

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• Asymptotic entropy and Green speed for random walks on countable groups
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• The Poisson formula for groups with hyperbolic properties
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