Recurrence of multiply-ended planar triangulations
Probability
2015-06-02 v1
Abstract
In this note we show that a bounded degree planar triangulation is recurrent if and only if the set of accumulation points of some/any circle packing of it is polar (that is, planar Brownian motion avoids it with probability 1). This generalizes a theorem of He and Schramm [6] who proved it when the set of accumulation points is either empty or a Jordan curve, in which case the graph has one end. We also show that this statement holds for any straight-line embedding with angles uniformly bounded away from 0.
Keywords
Cite
@article{arxiv.1506.00221,
title = {Recurrence of multiply-ended planar triangulations},
author = {Ori Gurel-Gurevich and Asaf Nachmias and Juan Souto},
journal= {arXiv preprint arXiv:1506.00221},
year = {2015}
}
Comments
8 pages, 1 figure