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.
| Original language | English |
|---|---|
| Article number | A05 |
| Pages (from-to) | 1-6 |
| Number of pages | 6 |
| Journal | Electronic Communications in Probability |
| Volume | 22 |
| DOIs | |
| State | Published - 2017 |
Bibliographical note
Publisher Copyright:© 2016 University of Washington. All rights reserved.
Keywords
- Circle packing
- Random walk
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