Abstract: Consider two configurations, C_1 and C_2, in Bernoulli bond percolation on a general graph G. Take the set S…
Abstract: Understanding the (near-)critical behavior of lattice models is one of the main challenges in statistical mechanics. A key approach…
Abstract: The disordered ferromagnet is a disordered version of the ferromagnetic Ising model in which the coupling constants are quenched…
Abstract: In this work, we study the random metric for the critical long-range percolation on . A recent work by…
Abstract: We derive an exact expression for the celebrated backbone exponent for 2D Bernoulli percolation at criticality. It turns out…
Abstract: We will describe forthcoming work in which we prove that branching Brownian motion in dimension four is governed by a…
Abstract: We prove Russo-Seymour-Welsh type crossing estimates for the FK-Ising model on general s-embeddings whose origami map has an asymptotic…
Abstract: The vacant set of the random walk on the torus is known to undergo a percolation phase transition at…
Abstract: Around 2008, Schramm conjectured that the critical probability p_c of a transitive graph is entirely determined by the local…
Abstract: A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000,…