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The components of the Wired Spanning Forest are recurrent
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  • Published: February 2003

The components of the Wired Spanning Forest are recurrent

  • Ben Morris1 

Probability Theory and Related Fields volume 125, pages 259–265 (2003)Cite this article

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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.

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Authors and Affiliations

  1. Statistics Department, University of California, Berkeley CA 94720, USA. Supported by an NSF Postdoctoral Fellowship. e-mail: morris@stat.berkeley.edu, , , , , , US

    Ben Morris

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  1. Ben Morris
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Received: 20 April 2001 / Revised version: 23 July 2002 / Published online: 14 November

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Morris, B. The components of the Wired Spanning Forest are recurrent. Probab Theory Relat Fields 125, 259–265 (2003). https://doi.org/10.1007/s00440-002-0236-0

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  • Issue Date: February 2003

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

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Keywords

  • Endpoint
  • Peris
  • Span Tree
  • Independent Interest
  • Effective Conductance
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