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.