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Recurrence of multiply-ended planar triangulations

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.

preprint2015arXivOpen access
Ori Gurel-GurevichAsaf NachmiasJuan Souto
math.PR
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Open access3 authors1 topic
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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Ori Gurel-GurevichAsaf NachmiasJuan Souto

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