Every planar graph with the Liouville property is amenable

DOI10.1002/rsa.20936zbMath1453.31015arXiv1502.02542OpenAlexW3032957580MaRDI QIDQ5136930

Angelos Georgakopoulos, Johannes Carmesin

Publication date: 30 November 2020

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.02542

zbMATH Keywords

harmonic functionplanar graphsinfinite graphelectrical networktransientrecurrentnon-amenableamenable planar graphsDirichlet harmonic functions circle packingnon amenable planar graphs

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Discrete potential theory (31C20)

Related Items (3)

Hyperbolicity vs. amenability for planar graphs ⋮ Random walk on random planar maps: spectral dimension, resistance and displacement ⋮ The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity

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