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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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. https://www.numdam.org/articles/10.4171/aihpd/27/
  • Woolls, Michael; Pryadko, Leonid P. Homology-changing percolation transitions on finite graphs, Journal of Mathematical Physics, Volume 63 (2022) no. 2 | DOI:10.1063/5.0036418
  • Jiang, Yi; Dumer, Ilya; Kovalev, Alexey A.; Pryadko, Leonid P. Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank, Journal of Mathematical Physics, Volume 60 (2019) no. 8 | DOI:10.1063/1.5039735

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