Ergodic and mixing random walks on locally compact groups

DOI10.1007/BF01450653zbMath0451.60011MaRDI QIDQ1148052

Joseph Max Rosenblatt

Publication date: 1981

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163540

zbMATH Keywords

ergodic random walkmixing random walksrandom walks on locally compact groups

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (31)

Factor and normal subgroup theorems for lattices in products of groups ⋮ Order structure on certain classes of ideals in group algebras and amenability ⋮ Poisson-Furstenberg boundary and growth of groups ⋮ Random walks on Baumslag-Solitar groups ⋮ Subshifts with slow complexity and simple groups with the Liouville property ⋮ Approximate lattices ⋮ Convergence of representation averages and of convolution powers ⋮ Ergodic sequences of averages of group representations ⋮ Realization of quantum group Poisson boundaries as crossed products ⋮ Amenability of groupoids and asymptotic invariance of convolution powers ⋮ Harmonic operators of ergodic quantum group actions ⋮ Convergence towards the end space for random walks on Schreier graphs ⋮ Poisson boundaries of monoidal categories ⋮ Boundaries of dense subgroups of totally disconnected groups ⋮ Arboreal structures on groups and the associated boundaries ⋮ Asymptotic behaviors of random walks on countable groups ⋮ Groups and dynamics: topology, measure, and Borel structure. Abstracts from the workshop held January 16--22, 2022 ⋮ The Liouville property and random walks on topological groups ⋮ Liouville property for groups and manifolds ⋮ Harmonic functions of linear growth on solvable groups ⋮ Amenability, Reiter's condition and Liouville property ⋮ POISSON BOUNDARIES OVER LOCALLY COMPACT QUANTUM GROUPS ⋮ Product set phenomena for countable groups ⋮ On mixing and ergodicity in locally compact motion groups ⋮ Product set phenomena for measured groups ⋮ Non-triviality of the Poisson boundary of random walks on the group of Monod ⋮ Choquet-Deny groups and the infinite conjugacy class property ⋮ Property A and the existence of a Markov process with a trivial Poisson boundary ⋮ Averaging sequences and modulated ergodic theorems for weakly almost periodic group representations ⋮ Probability measures on groups and some related ideals in group algebras ⋮ Amenability and the Liouville property

Cites Work

• Mixing properties of Markov operators and ergodic transformations, and ergodicity of Cartesian products
• Convolutions, means, and spectra
• Full Banach Mean Values on Countable groups.
• Large Symmetric Sets in Amenable Groups and the Individual Ergodic Theorem
• On Iterates of Convolutions
• On Locally Compact Groups with Invariant Means
• On mixing in infinite measure spaces
• Invariant Measures and Growth Conditions
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