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.
Bibliographical noteFunding Information:
The authors wish to thank Asaf Nachmias for many useful discussions and comments.
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