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2017 Recurrence of multiply-ended planar triangulations
Ori Gurel-Gurevich, Asaf Nachmias, Juan Souto
Electron. Commun. Probab. 22(none): 1-6 (2017). DOI: 10.1214/16-ECP4418

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 $0$.

Citation

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Ori Gurel-Gurevich. Asaf Nachmias. Juan Souto. "Recurrence of multiply-ended planar triangulations." Electron. Commun. Probab. 22 1 - 6, 2017. https://doi.org/10.1214/16-ECP4418

Information

Received: 12 July 2015; Accepted: 17 May 2016; Published: 2017
First available in Project Euclid: 6 January 2017

zbMATH: 1360.52013
MathSciNet: MR3607800
Digital Object Identifier: 10.1214/16-ECP4418

Subjects:
Primary: 05C81, 52C26

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