Mathematical Physics Seminar

Percolation is one of most simple models which exhibits a phase transition. The determination of the threshold for this phase transition is usually quite difficult. It is the central problem of percolation theory. The relation between percolation and quantum error correction has been exploited in quantum information theory. In the present work, we propose to go in the other direction. We derive new bounds on the percolation threshold of hyperbolic graphs based on results of quantum information. This leads to the most precise upper bound on the percolation threshold of these graphs, improving bounds of Benjamini and Schramm. Join work with Gilles Zémor. Annales de l'Institut Henri Poincaré D, Vol. 3, Issue 2, pp. 139-161. 2016 https://arxiv.org/abs/1408.4031