'Stunning' percolation proof solves decades-old puzzle about phase transitions

A team of mathematicians at ETH Zurich—including Sahar Diskin, Philip Easo, Ritvik Ramanan Radhakrishnan, Benny Sudakov, and Vincent Tassion—produced a proof that determines the speed at which a percolation network becomes dominated by a giant connected component as the edge-opening probability exceeds the critical threshold. Their argument applies uniformly to a wide class of graphs, resolving a longstanding question about the rate of the phase transition first modeled by Broadbent and Hammersley in the 1950s.