Ariel Yadin (Ben-Gurion University)

Thursday, November 19, 2020, 11:10 – 12:00, Online

Please Note the Unusual Place!


In 1920 Ising showed that the infinite line Z does not admit a phase transition for percolation. In fact, no “one-dimensional” graph does. However, it has been asked if this is the only obstruction. Specifically, Benjamini & Schramm conjectured in 1996 that any graph with isoperimetric dimension greater than 1 will have a non-trivial phase transition.
We prove this conjecture for all dimensions greater than 4. When the graph is transitive this solves the question completely, since low-dimensional transitive graphs are quasi-isometric to Cayley graphs, which we can classify thanks to Gromov’s theorem. This is joint work with H. Duminil-Copin, S. Goswami, A. Raufi, F. Severo.