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

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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.

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Acknowledgements

The authors wish to thank Asaf Nachmias for many useful discussions and comments.

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Authors and Affiliations

  1. Einstein Institute of Mathematics, The Hebrew University of Jerusalem Givat Ram, Jerusalem, 91904, Israel

    Ori Gurel-Gurevich

  2. School of Mathematical Sciences, Tel Aviv University Ramat Aviv, Tel Aviv, 6997801, Israel

    Matan Seidel

Authors
  1. Ori Gurel-Gurevich
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  2. Matan Seidel
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Correspondence to Ori Gurel-Gurevich.

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Gurel-Gurevich, O., Seidel, M. Recurrence of a weighted random walk on a circle packing with parabolic carrier. Isr. J. Math. 247, 547–591 (2022). https://doi.org/10.1007/s11856-022-2286-6

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  • DOI: https://doi.org/10.1007/s11856-022-2286-6

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