UNIFORM SPANNING FORESTS OF PLANAR GRAPHS
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Publication:5194701
DOI10.1017/FMS.2019.14zbMATH Open1422.60022arXiv1603.07320OpenAlexW2972331908MaRDI QIDQ5194701
Author name not available (Why is that?)
Publication date: 17 September 2019
Published in: (Search for Journal in Brave)
Abstract: We prove that the free uniform spanning forest of any bounded degree proper plane graph is connected almost surely, answering a question of Benjamini, Lyons, Peres and Schramm. We provide a quantitative form of this result, calculating the critical exponents governing the geometry of the uniform spanning forests of transient proper plane graphs with bounded degrees and codegrees. We find that the same exponents hold universally over this entire class of graphs provided that measurements are made using the hyperbolic geometry of their circle packings rather than their usual combinatorial geometry.
Full work available at URL: https://arxiv.org/abs/1603.07320
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