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}
}