UNIFORM SPANNING FORESTS OF PLANAR GRAPHS

Tom Hutchcroft, Asaf Nachmias

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish
Article numbere29
JournalForum of Mathematics, Sigma
Volume7
DOIs
StatePublished - 2019

Funding

FundersFunder number
Horizon 2020 Framework Programme676970
Horizon 2020 Framework Programme

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