Strongly approximately transitive group actions, the Choquet-Deny theorem, and polynomial growth

DOI10.2140/pjm.1994.165.115zbMath0881.22004OpenAlexW2035182985MaRDI QIDQ1338921

Wojciech Jaworski

Publication date: 2 February 1998

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1994.165.115

zbMATH Keywords

homogeneous spacespolynomial growthrandom walksprobability measurelocally compact groupsamenable groupsChoquet-Deny theoremBorel \(G\)-spacenonamenable grouppurely atomicstrongly approximately transitive

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) General groups of measure-preserving transformations (28D15) Boundary theory for Markov processes (60J50) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

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Poisson boundaries of II₁ factors ⋮ Boundaries of reduced \(C^\ast\)-algebras of discrete groups ⋮ A Poisson formula for solvable Lie groups ⋮ Random walks on almost connected locally compact groups: Boundary and convergence ⋮ Subalgebras, subgroups, and singularity ⋮ Arboreal structures on groups and the associated boundaries ⋮ Stabilizers of ergodic actions of lattices and commensurators ⋮ Contractive spaces and relatively contractive maps ⋮ Weak mixing properties for non-singular actions ⋮ Stabilizers of actions of lattices in products of groups ⋮ A normal subgroup theorem for commensurators of lattices ⋮ Recurrence for Stationary Group Actions ⋮ Product set phenomena for measured groups ⋮ Furstenberg maps for CAT(0) targets of finite telescopic dimension ⋮ Bounded harmonic functions on connected solvable Lie groups and existence of an invariant measure ⋮ Random walks on convergence groups

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