Crossing estimates and convergence of Dirichlet functions along random walk and diffusion paths

DOI10.1214/aop/1022677392zbMath0945.60063OpenAlexW2032573808MaRDI QIDQ1807208

Yuval Peres, Alano Ancona, Russell Lyons

Publication date: 9 November 1999

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

Full work available at URL: https://doi.org/10.1214/aop/1022677392

zbMATH Keywords

manifoldsMarkov chaindiffusionsrandom walkalmost sure convergenceDirichlet energycrossing

Mathematics Subject Classification ID

Strong limit theorems (60F15) Dirichlet forms (31C25) Probabilistic potential theory (60J45)

Related Items (13)

Determination of the walk dimension of the Sierpiński gasket without using diffusion ⋮ Harmonic analysis invariants for infinite graphs via operators and algorithms ⋮ Recurrence of random walk traces ⋮ A discrete Gauss-Green identity for unbounded Laplace operators, and the transience of random walks ⋮ Recurrence of Markov chain traces ⋮ Random walks and induced Dirichlet forms on self-similar sets ⋮ Random walks and Kuramochi boundaries of infinite networks ⋮ A Dirichlet principle for non reversible Markov chains and some recurrence theorems ⋮ Harmonic Dirichlet functions on planar graphs ⋮ Monopoles, dipoles, and harmonic functions on Bratteli diagrams ⋮ Boundaries of planar graphs, via circle packings ⋮ Unimodular hyperbolic triangulations: circle packing and random walk ⋮ Parabolicity, the divergence theorem for \(\delta\)-subharmonic functions and applications to the Liouville theorems for harmonic maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ideal boundary limit of discrete Dirichlet functions
• Decomposition of Dirichlet processes and its applications
• Dirichlet forms and symmetric Markov processes
• Potential theory on infinite networks
• The limits of stochastic integrals of differential forms
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• Les fonctions surharmoniques associées à un opérateur elliptique du second ordre à coefficients discontinus
• Finely harmonic functions
• Random walks and harmonic functions on infinite planar graphs using square tilings
• Boundary properties of functions with finite Dirichlet integrals
• Conditional brownian motion and the boundary limits of harmonic functions
• Convergence to Ends for Random Walks on the Automorphism Group of a Tree

This page was built for publication: Crossing estimates and convergence of Dirichlet functions along random walk and diffusion paths