Probability Theory and Related Fields

, Volume 125, Issue 2, pp 259–265

The components of the Wired Spanning Forest are recurrent

  • Ben Morris

DOI: 10.1007/s00440-002-0236-0

Cite this article as:
Morris, B. Probab Theory Relat Fields (2003) 125: 259. doi:10.1007/s00440-002-0236-0


 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.

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