UVictoria Probability and Dynamics Seminar: 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 idea from computer science and fits on one page.

Our new approach resolves a conjecture of Babson of Benjamini from 1999 and provides a simpler proof of the celebrated result of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin that percolation on any non-one-dimensional transitive graph undergoes a non-trivial phase transition.