Prof. R. Morris (IMPA, Brasile)
Titolo: Universality for bootstrap percolation in two dimensions
Venerdi' 29 Maggio 2015 ORE 14:30
Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre AULA 211 (Largo San L. Murialdo,1 - Palazzina C)
Abstract: In the classical r-neighbour bootstrap percolation model on a graph G, vertices are initially infected independently at random with probability p, and subsequently vertices become infected as soon as they have at least r already-infected neighbours. In this talk we will discuss a vast generalization of this model on the lattice Z^d, which was introduced recently by Bollobas, Smith and Uzzell. Somewhat surprisingly, it turns out that in two dimensions there are only a small number of possible behaviours. We will discuss what is known so far, and the many open questions in higher dimensions. This is joint work with Bela Bollobas, Hugo Duminil-Copin and Paul Smith.