## The Annals of Probability

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

### Percolation on a product of two trees

#### 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 It relies on an unpublished lemma of Oded Schramm.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