Recurrence of a Weighted Random Walk on a Circle Packing with Parabolic Carrier

Abstract

In this paper we show that given a circle packing of an infinite planar triangulation such that its carrier is parabolic, placing weights on the edges according to a certain natural way introduced by Dubejko, makes the random walk recurrent. We also propose a higher-dimensional analogue of the Dubejko weights.

arXiv comment26 pages, 9 figures