The components of the Wired Spanning Forest are recurrent
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Probability Theory and Related Fields
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.
Digital Object Identifier (DOI)
Morris, Ben, "The components of the Wired Spanning Forest are recurrent" (2003). KIP Articles. 6695.