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.