The components of the Wired Spanning Forest are recurrent
- Cite this article as:
- Morris, B. Probab Theory Relat Fields (2003) 125: 259. doi:10.1007/s00440-002-0236-0
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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.