The components of the Wired Spanning Forest are recurrent |
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Authors: | Ben Morris |
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Affiliation: | (1) Statistics Department, University of California, Berkeley CA 94720, USA. Supported by an NSF Postdoctoral Fellowship. e-mail: morris@stat.berkeley.edu, US |
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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. Received: 20 April 2001 / Revised version: 23 July 2002 / Published online: 14 November |
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