Uniform spanning forests
Benjamini, Itai ; Lyons, Russell ; Peres, Yuval ; Schramm, Oded
Ann. Probab., Tome 29 (2001) no. 1, p. 1-65 / Harvested from Project Euclid
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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 $\mathbb{Z}^d$ and that they give a single tree iff $d 0$, the union of the WSF and Bernoulli percolation with parameter $\epsilon$ 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.
Publié le : 2001-02-14
Classification:  Spanning trees,  Cayley graphs,  electrical networks,  harmonic Dirichlet functions,  amenability,  percolation,  loop-erased walk,  60D05,  05C05,  60B99,  20F32,  31C20,  05C80 
@article{1008956321,
     author = {Benjamini, Itai and Lyons, Russell and Peres, Yuval and Schramm, Oded},
     title = {Uniform spanning forests},
     journal = {Ann. Probab.},
     volume = {29},
     number = {1},
     year = {2001},
     pages = { 1-65},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1008956321}
}

Benjamini, Itai; Lyons, Russell; Peres, Yuval; Schramm, Oded. Uniform spanning forests. Ann. Probab., Tome 29 (2001) no. 1, pp.  1-65. http://gdmltest.u-ga.fr/item/1008956321/