Annales de l’Institut Henri Poincaré D


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Volume 3, Issue 2, 2016, pp. 139–161
DOI: 10.4171/AIHPD/27

Published online: 2016-05-19

A homological upper bound on critical probabilities for hyperbolic percolation

Nicolas Delfosse[1] and Gilles Zémor[2]

(1) Université de Sherbrooke, Canada
(2) Université de Bordeaux, Talence, France

We study bond percolation for a family of infinite hyperbolic graphs. We relate percolation to the appearance of homology in finite versions of these graphs. As a consequence, we derive an upper bound on the critical probabilities of the infinite graphs.

Keywords: Percolation, critical probability, hyperbolic lattice, homology

Delfosse Nicolas, Zémor Gilles: A homological upper bound on critical probabilities for hyperbolic percolation. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 3 (2016), 139-161. doi: 10.4171/AIHPD/27