Electronic Journal of Probability

Ends in Uniform Spanning Forests

Russell Lyons, Benjamin Morris, and Oded Schramm

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819131

Digital Object Identifier
doi:10.1214/EJP.v13-566

Mathematical Reviews number (MathSciNet)
MR2448128

Zentralblatt MATH identifier
1191.60016

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

Keywords
Spanning trees Cayley graphs

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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