Asymptotic entropy and Green speed for random walks on countable groups

DOI10.1214/07-AOP356zbMath1146.60008arXivmath/0607467OpenAlexW2102970554MaRDI QIDQ2427060

Pierre Mathieu, Sébastien Blachère, Peter Haïssinsky

Publication date: 15 May 2008

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607467

zbMATH Keywords

rate of escapeasymptotic entropyrandom walks on groupsGreen speed

Mathematics Subject Classification ID

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

Related Items (23)

Catching homologies by geometric entropy ⋮ Asymptotic Word Length of Random Walks on HNN Extensions ⋮ Optimal Control for Diffusions on Graphs ⋮ Deviation inequalities for random walks ⋮ CUTOFF AT THE ENTROPIC TIME FOR RANDOM WALKS ON COVERED EXPANDER GRAPHS ⋮ Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes ⋮ On the strong Liouville property of covering spaces ⋮ Local limit theorem for a Markov additive process on with a null recurrent internal Markov chain ⋮ Most transient random walks have infinitely many cut times ⋮ Asymptotic entropy of the ranges of random walks on discrete groups ⋮ Quasi-Fuchsian vs negative curvature metrics on surface groups ⋮ Asymptotic behaviors of random walks on countable groups ⋮ Random walks on directed covers of graphs ⋮ Asymptotic entropy of transformed random walks ⋮ Hausdorff spectrum of harmonic measure ⋮ Central limit theorems for Gromov hyperbolic groups ⋮ Positive harmonic functions on groups and covering spaces ⋮ Differentiating the entropy of random walks on hyperbolic groups ⋮ The boundary of the range of a random walk and the Følner property ⋮ Asymptotic entropy of random walks on Fuchsian buildings and Kac-Moody groups ⋮ Poisson boundaries of lamplighter groups: proof of the Kaimanovich-Vershik conjecture ⋮ Entropy and drift for word metrics on relatively hyperbolic groups ⋮ Entropy and drift for Gibbs measures on geometrically finite manifolds

Cites Work

• Markoff chains and Martin boundaries
• On laws of large numbers for random walks
• Internal diffusion limited aggregation on discrete groups having exponential growth
• Linear drift and Poisson boundary for random walks
• Manifolds of nonpositive curvature
• Random walks on discrete groups: Boundary and entropy
• Tree-indexed random walks on groups and first passage percolation
• On drift and entropy growth for random walks on groups
• Ultracontractivity and Nash type inequalities
• Boundary and entropy of space homogeneous Markov chains
• Random walks on discrete groups of polynomial volume growth
• Dynamic theory of growth in groups: Entropy, boundaries, examples
• Random Walks on Infinite Graphs and Groups
• Harmonic measures versus quasiconformal measures for hyperbolic groups
• BOUNDARY THEORY OF MARKOV PROCESSES (THE DISCRETE CASE)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Asymptotic entropy and Green speed for random walks on countable groups