Abstract: Consider long-range percolation on , where there is an edge between two points and with probability asymptotic to ,…
Abstract: Consider Ising model in three and higher dimensions with i.i.d. Gaussian externel field. We are going to show that…
Abstract: We will consider FK percolation on with infinite range interactions of the form where is a norm on and is…
Abstract: A few years ago Duminil-Copin, Goswami, Rodriguez and Severo established the sharpness of the phase transition for level-set percolation of the…
Abstract: A 1-independent bond percolation model on a graph is a probability distribution on the spanning subgraphs of in which,…
Abstract: We will report on our joint work with C. Garban and try to do it form the point of…
Abstract: How long does a self-avoiding walk on a finite transitive > graph have to be before it `feels’ the effect…
Abstract: The talk will focus on large-scale metric properties of random graphs obtained from by way of long range percolation.…
Abstract: The threshold of an increasing property of a random set (or random graph) is the density at which a random…
Abstract: The Universality Conjecture of Bollobás, Duminil-Copin, Morris and Smith states that every d-dimensional monotone cellular automaton is a member…