Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published November 2016 | Submitted + Published
Journal Article Open

Wired cycle-breaking dynamics for uniform spanning forests


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 [Ann. Probab. 29 (2001) 1–65]. 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.

Additional Information

© 2016 Institute of Mathematical Statistics. Received April 2015; revised September 2015. We thank Tel Aviv University for its hospitality while this work was completed.We also thank Omer Angel and Asaf Nachmias for many valuable comments on earlier versions of the paper, and thank the referee and Associate Editor for their comments and suggestions.

Attached Files

Published - 15-AOP1063.pdf

Submitted - 1504.03928.pdf


Files (545.7 kB)
Name Size Download all
358.2 kB Preview Download
187.6 kB Preview Download

Additional details

August 18, 2023
October 20, 2023