Percolation on a product of two trees

Details Percolation on a product of two trees Percolation on a product of two trees

2010-03-26

arxiv.org/abs/1003.5240v3

Annals of Probability 2011, Vol. 39, No. 5, 1864-1895

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP618 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP618

We show that critical percolation on a product of two regular trees of degree
$\ge$ 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unpublished lemma of Oded Schramm.

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