文章基本信息

标题：Recurrence of multiply-ended planar triangulations
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作者：Ori Gurel-Gurevich ; Asaf Nachmias ; Juan Souto 等
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2017
卷号：22
DOI：10.1214/16-ECP4418
语种：English
出版社：Electronic Communications in Probability
摘要：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 $0$.