JournalsaihpdVol. 3, No. 2pp. 139–161

A homological upper bound on critical probabilities for hyperbolic percolation

  • Nicolas Delfosse

    Université de Sherbrooke, Canada

  • Gilles Zémor

    Université de Bordeaux, Talence, France
A homological upper bound on critical probabilities for hyperbolic percolation cover
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Abstract

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.

Cite this article

Nicolas Delfosse, Gilles Zémor, A homological upper bound on critical probabilities for hyperbolic percolation. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 3 (2016), no. 2, pp. 139–161

DOI 10.4171/AIHPD/27