The Annals of Probability

Percolation on a product of two trees

Gady Kozma

Full-text: Open access

Abstract

We show that critical percolation on a product of two regular trees of degree ≥ 3 satisfies the triangle condition. The proof does not examine the degrees of vertices and is not “perturbative” in any sense. It relies on an unpublished lemma of Oded Schramm.

Article information

Source
Ann. Probab. Volume 39, Number 5 (2011), 1864-1895.

Dates
First available in Project Euclid: 18 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.aop/1318940784

Digital Object Identifier
doi:10.1214/10-AOP618

Mathematical Reviews number (MathSciNet)
MR2884876

Zentralblatt MATH identifier
1243.60078

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60B99: None of the above, but in this section

Keywords
Percolation on groups triangle condition nonamenable groups mean-field product of trees

Citation

Kozma, Gady. Percolation on a product of two trees. Ann. Probab. 39 (2011), no. 5, 1864--1895. doi:10.1214/10-AOP618. https://projecteuclid.org/euclid.aop/1318940784


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