Philip Easo

The classical Peierls argument establishes that percolation on a graph G has a non-trivial (uniformly) percolating phase if G has “not too many small cutsets”. Severo, Tassion, and I have recently proved the converse. Our argument is inspired by an...

Around 2008, Schramm conjectured that the critical probability pc of a transitive graph is entirely determined by the local geometry of the graph, subject to the global constraint that pc1. In other words, if Gn is a sequence of transitive graphs...