A homological upper bound on critical probabilities for hyperbolic percolation
Annales de l’Institut Henri Poincaré D, Tome 3 (2016) no. 2, pp. 139-161.

We study bond percolation for a family of in�finite 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 infi�nite graphs.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/27
Classification : 82-XX, 60-XX
Mots-clés : Percolation, critical probability, hyperbolic lattice, homology 
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     title = {A homological upper bound on critical probabilities for hyperbolic percolation},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {139--161},
     volume = {3},
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     doi = {10.4171/aihpd/27},
     mrnumber = {3506075},
     zbl = {1342.82075},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/27/}
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Delfosse, Nicolas; Zémor, Gilles. A homological upper bound on critical probabilities for hyperbolic percolation. Annales de l’Institut Henri Poincaré D, Tome 3 (2016) no. 2, pp. 139-161. doi : 10.4171/aihpd/27. http://archive.numdam.org/articles/10.4171/aihpd/27/

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