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

Daniel Boivin; Clément Rau

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arXiv · 1111.5326

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

Daniel Boivin·Clément Rau

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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 $\Z^d$, $d\geq 3$, 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 $\Z^2$. This is proved using results of Barlow (2004).

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Daniel Boivin, Clément Rau. 2011-11-22. Existence of the harmonic measure for random walks on graphs and in random environments. https://arxiv.org/abs/1111.5326

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