Recurrence of multiply-ended planar triangulations

Ori Gurel-Gurevich, Asaf Nachmias, Juan Souto

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish
Article numberA05
Pages (from-to)1-6
Number of pages6
JournalElectronic Communications in Probability
StatePublished - 2017


FundersFunder number
Horizon 2020 Framework Programme676970


    • Circle packing
    • Random walk


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