Existence of the harmonic measure for random walks on graphs and in random environments

2011/11/22 by Daniel Boivin, Boivin, Daniel, Clément Rau +1 · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.1111.5326

openalex publication_date 2011/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on \Z^d, d≥ 3, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of \Z². This is proved using results of Barlow (2004).

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