Uniform Spanning Forests of Planar Graphs
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Hutchcroft, Tom
Nachmias, Asaf
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.
Description
Keywords
60D05 (primary), 05C10 (secondary)
Journal Title
Forum of Mathematics, Sigma
Conference Name
Journal ISSN
2050-5094
2050-5094
2050-5094
Volume Title
Publisher
Cambridge University Press
Publisher DOI
Rights
All rights reserved
Sponsorship
This project was supported by NSERC Discovery grant 418203, ISF grant 1207/15, and ERC starting grant RADNGEOM 676970.