Uniform spanning forests

@article{Benjamini2001UniformSF,
  title={Uniform spanning forests},
  author={Itai Benjamini and Russell Lyons and Yuval Peres and Oded Schramm},
  journal={Annals of Probability},
  year={2001},
  volume={29},
  pages={1-65}
}
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 Z d and that they give a single tree iff d ≤ 4. In the present work, we extend Pemantle's alternative to general graphs and exhibit further connections of uniform spanning forests to random walks, potential… 

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