"MÜNCHHAUSEN TRICK" AND AMENABILITY OF SELF-SIMILAR GROUPS

DOI10.1142/S0218196705002694zbMath1168.20308OpenAlexW2045706494MaRDI QIDQ3379477

Vadim A. Kaimanovich

Publication date: 6 April 2006

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196705002694

zbMATH Keywords

random walksamenabilityLiouville propertyasymptotic entropyrooted treesGrigorchuk groupself-similar groupsinternal degrees of freedomBasilica groupiterated monodromy groups

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Asymptotic properties of groups (20F69) Groups acting on trees (20E08) Means on groups, semigroups, etc.; amenable groups (43A07) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (15)

Poisson-Furstenberg boundary and growth of groups ⋮ Subshifts with slow complexity and simple groups with the Liouville property ⋮ Amenability and non-uniform growth of some directed automorphism groups of a rooted tree ⋮ On amenability of automata groups. ⋮ Homomorphisms to \(\mathbb R\) constructed from random walks ⋮ Self-similar groups and holomorphic dynamics: renormalization, integrability, and spectrum ⋮ Distortion of imbeddings of groups of intermediate growth into metric spaces ⋮ Asymptotic behaviors of random walks on countable groups ⋮ Behaviors of entropy on finitely generated groups ⋮ Diameters, distortion, and eigenvalues ⋮ Some topics in the dynamics of group actions on rooted trees. ⋮ Blocks of monodromy groups in complex dynamics ⋮ Dual graphs and modified Barlow-Bass resistance estimates for repeated barycentric subdivisions ⋮ Amenable groups without finitely presented amenable covers ⋮ Amenability via random walks.

Cites Work

• Random walks on discrete groups: Boundary and entropy
• Liouville property for groups and manifolds
• The Poisson boundary of covering Markov operators
• Hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks
• Boundary behavior for groups of subexponential growth.
• Random walks with internal degrees of freedom
• The lamplighter group as a group generated by a 2-state automaton, and its spectrum

This page was built for publication: "MÜNCHHAUSEN TRICK" AND AMENABILITY OF SELF-SIMILAR GROUPS