Recurrence of a weighted random walk on a circle packing with parabolic carrier (Q2143248)

The main goal of the authors in this paper is to prove the following result. Suppose that \(\Omega\subseteq \mathbb{R}^2\) is a parabolic domain. Then for any circle-packed infinite triangulation of \(\Omega\), the Dubejko-weighted random walk is recurrent. A higher-dimensional analogue of the Dubejko weights is introduced and discussed.