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We study uniform spanning forest measures on infinite graphs, which are weak limits of uniform spanning tree measures from finite subgraphs. These limits can be taken with free (FSF) or wired (WSF) boundary conditions. Pemantle proved that the free and wired spanning forests coincide in Zᵈ and that they give a single tree iff d 0, the union of the WSF and Bernoulli percolation with parameter is connected. Harmonic measure from infinity is shown to exist on any recurrent proper planar graph with finite codegrees. We also present numerous open problems and conjectures.
Benjamini et al. (Thu,) studied this question.