Amenability via random walks.
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Publication:814687
DOI10.1215/S0012-7094-05-13012-5zbMath1104.43002arXivmath/0305262MaRDI QIDQ814687
Bálint Virág, Laurent Bartholdi
Publication date: 7 February 2006
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0305262
Sums of independent random variables; random walks (60G50) Generators, relations, and presentations of groups (20F05) Means on groups, semigroups, etc.; amenable groups (43A07)
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Cites Work
- Amenable semigroups
- On amenability of group algebras. I.
- Elementary amenable groups
- Boundary and entropy of space homogeneous Markov chains
- Full Banach Mean Values on Countable groups.
- "MÜNCHHAUSEN TRICK" AND AMENABILITY OF SELF-SIMILAR GROUPS
- An example of a finitely presented amenable group not belonging to the classEG
- Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces
- ON A TORSION-FREE WEAKLY BRANCH GROUP DEFINED BY A THREE STATE AUTOMATON
- Random Walks on Infinite Graphs and Groups
- Probability
- Unnamed Item
- Unnamed Item
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