English

Ends in Uniform Spanning Forests

Probability 2010-04-27 v2

Abstract

It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience.

Keywords

Cite

@article{arxiv.0706.0358,
  title  = {Ends in Uniform Spanning Forests},
  author = {Russell Lyons and Benjamin J. Morris and Oded Schramm},
  journal= {arXiv preprint arXiv:0706.0358},
  year   = {2010}
}
R2 v1 2026-06-21T08:34:43.458Z