@article{678b62497cc94f3282f44f80cb465747,

title = "Recurrence of multiply-ended planar triangulations",

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.",

keywords = "Circle packing, Random walk",

author = "Ori Gurel-Gurevich and Asaf Nachmias and Juan Souto",

note = "Publisher Copyright: {\textcopyright} 2016 University of Washington. All rights reserved.",

year = "2017",

doi = "10.1214/16-ECP4418",

language = "אנגלית",

volume = "22",

pages = "1--6",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

}