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

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

2011-11-22

arxiv.org/abs/1111.5326v2

Mathematics

Probability

25 p. and 2 figures

Scientific paper

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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