On the stability of the behavior of random walks on groups

DOI10.1007/bf02921994zbMath0988.60517MaRDI QIDQ6205147

Christophe Pittet, Laurent Saloff-Coste

Publication date: 23 September 1998

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

Cayley graphsheat kernelcompact manifoldsrandom walkquasi-isometry

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Diffusion processes and stochastic analysis on manifolds (58J65) Harmonic analysis on general compact groups (43A77)

Related Items

Spectral properties of a class of random walks on locally finite groups ⋮ Long range random walks and associated geometries on groups of polynomial growth ⋮ The Liouville property and Hilbertian compression ⋮ Metabelian groups with large return probability

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gaussian estimates for Markov chains and random walks on groups
• Rough isometries, and combinatorial approximations of geometries of non- compact Riemannian manifolds
• Uniformly elliptic operators on Riemannian manifolds
• Puissances d'un opérateur régularisant. (Powers of a regularizing operator)
• Upper bounds for symmetric Markov transition functions
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Brownian motion and transient groups
• On-diagonal lower bounds for heat kernels and Markov chains
• Ultracontractivity and Nash type inequalities
• Isometric Riemannian manifolds at infinity
• On groups with full Banach mean value
• Some Theorems Concerning Brownian Motion
• Symmetric Random Walks on Groups
• Matrix Analysis
• Amenability and the spectrum of the Laplacian
• A note on the isoperimetric constant
• A Lower Estimate for Central Probabilities on Polycyclic Groups
• Random Walks on Infinite Graphs and Groups - a Survey on Selected topics
• The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups