Title

The components of the Wired Spanning Forest are recurrent

Author

Ben Morris

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Publication Date

1-1-2003

Publication Title

Probability Theory and Related Fields

Volume Number

125

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.

Document Type

Article

Digital Object Identifier (DOI)

https://doi.org/10.1007/s00440-002-0236-0

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