Wired Cycle-Breaking Dynamics for Uniform Spanning Forests
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Hutchcroft, Tom
Abstract
We prove that every component of the wired uniform spanning forest (WUSF) is one-ended almost surely in every transient reversible random graph, removing the bounded degree hypothesis required by earlier results. We deduce that every component of the WUSF is one-ended almost surely in every supercritical Galton-Watson tree, answering a question of Benjamini, Lyons, Peres and Schramm. Our proof introduces and exploits a family of Markov chains under which the oriented WUSF is stationary, which we call the wired cycle-breaking dynamics.
Description
Keywords
math.PR, math.PR
Journal Title
Ann. Probab.
Conference Name
Journal ISSN
0091-1798
Volume Title
44
Publisher
Institute of Mathematical Statistics