Abstract: We solved the longstanding density conjecture for activated random walk by proving that several variants have the same critical…
Abstract: In Catalan percolation, one declares the edges for \emph{occupied} and each edge with \emph{open} independently with probability . For…
Abstract: The classical Peierls argument establishes that percolation on a graph G has a non-trivial (uniformly) percolating phase if G…
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…