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On which graphs are all random walks in random environments transient?

Robin Pemantle·Yuval Peres
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Abstract

An infinite graph G has the property that a random walk in random environment on G defined by i.i.d. resistances with any common distribution is almost surely transient, if and only if for some p<1, simple random walk is transient on a percolation cluster of G under bond percolation with parameter p.

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Robin Pemantle, Yuval Peres. 2004-04-05. On which graphs are all random walks in random environments transient?. https://arxiv.org/abs/math/0404087

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