Electronic Journal of Probability

Ends in Uniform Spanning Forests

Russell Lyons, Benjamin Morris, and Oded Schramm

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It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience.

Article information

Electron. J. Probab., Volume 13 (2008), paper no. 58, 1702-1725.

Accepted: 21 September 2008
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60B99: None of the above, but in this section
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 20F32

Spanning trees Cayley graphs

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Lyons, Russell; Morris, Benjamin; Schramm, Oded. Ends in Uniform Spanning Forests. Electron. J. Probab. 13 (2008), paper no. 58, 1702--1725. doi:10.1214/EJP.v13-566. https://projecteuclid.org/euclid.ejp/1464819131

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