Ivailo Hartarsky
(ENS, France)

Titolo: Bootstrap percolation : subcritical universality class and
oriented percolation

Mercoledi' 24 Ottobre 2018 ORE 16:00

Dipartimento di Matematica e Fisica 
Universita' degli Studi Roma Tre
Largo San Leonardo Murialdo,1 - Pal.C - Aula 211

Abstract
Bootstrap percolation is a wide class of deterministic monotone
cellular automata with random initial state closely related to several
other statistical physics models such as the kinetically constrained
spin models for the spin glass transition. There are three
`universality classes' of bootstrap percolation in two dimensions. Of
them the `subcritical' ones   those exhibiting a non-trivial phase
transition   are by far the most poorly understood. In this work we
develop a first approach for studying them.
We will start with a gentle introduction to the field and its
universality picture to provide the necessary background. We will then
introduce the main new notion of critical density and state our main
result. We will then illustrate the method by applications to concrete
examples yielding  new and old results in the area. The approach
establishes and exploits a tight connection with a new generalization
of classical oriented percolation, whose further study will have a
direct impact on bootstrap percolation. The talk will be based on the
preprint arxiv:1806.11405.