Probability Theory and Related Fields

, Volume 125, Issue 2, pp 259–265

The components of the Wired Spanning Forest are recurrent

  • Ben Morris

Abstract

 We show that a.s. all of the connected components of the Wired Spanning Forest are recurrent, proving a conjecture of Benjamini, Lyons, Peres and Schramm. Our analysis relies on a simple martingale involving the effective conductance between the endpoints of an edge in a uniform spanning tree. We believe that this martingale is of independent interest and will find further applications in the study of uniform spanning trees and forests.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ben Morris
    • 1
  1. 1.Statistics Department, University of California, Berkeley CA 94720, USA. Supported by an NSF Postdoctoral Fellowship. e-mail: morris@stat.berkeley.eduUS

Personalised recommendations