The Liouville and the intersection properties are equivalent for planar graphs

DOI10.1214/ECP.v17-1913zbMath1252.05208arXiv1203.4002MaRDI QIDQ456273

Itai Benjamini, Nicolas Curien, Angelos Georgakopoulos

Publication date: 23 October 2012

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.4002

zbMATH Keywords

random walksplanar graphsLiouville propertyintersection

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Random walks on graphs (05C81)

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Harnack inequality and one-endedness of UST on reversible random graphs ⋮ Planar stochastic hyperbolic triangulations ⋮ Uniform spanning forests on biased Euclidean lattices ⋮ Hyperbolic and parabolic unimodular random maps ⋮ The boundary of a square tiling of a graph coincides with the Poisson boundary

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