Green function estimates and their applications to the intersections of symmetric random walks

DOI10.1016/0304-4149(93)90106-EzbMath0810.60064OpenAlexW2071973430MaRDI QIDQ1313126

Xian Yin Zhou

Publication date: 26 January 1994

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(93)90106-e

zbMATH Keywords

Harnack inequalityGreen functionsWiener testrandom walks on graphseffective resistance

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Sample path properties (60G17)

Related Items

On the range of reversible random walks on \(Z^ 2\) in a random environment ⋮ An optimal error estimate in stochastic homogenization of discrete elliptic equations ⋮ Isoperimetric Inequalities and Decay of Iterated Kernels for Almost-transitive Markov Chains ⋮ Inequalities forp-superharmonic functions on networks ⋮ An optimal variance estimate in stochastic homogenization of discrete elliptic equations ⋮ An intersection property of the simple random walks in \(Z^ d\) ⋮ Spectral homogenization of reversible random walks on \(\mathbb Z^d\) in a random environment.

Cites Work

• Unnamed Item
• Unnamed Item
• The construction of Brownian motion on the Sierpinski carpet
• Random walks on graphs, electric networks and fractals
• A self-avoiding random walk
• Dirichlet forms on fractals: Poincaré constant and resistance
• Potentials and the random walk
• Some intersection properties of random walk paths
• On functions of bounded mean oscillation
• On Harnack's theorem for elliptic differential equations