Uniform upper bound on the percolation threshold for Cayley graphs

Abstract:   We prove that there is a uniform upper bound u<1 on the percolation threshold for any Cayley graph that is not one-dimensional. This improves on a recent result by Duminil-Copin, Goswami, Raoufi, Severo and Yadin who obtained the non-triviality of the percolation threshold.

This talk is based on joint work with Franco Severo.