Universality for critical kinetically constrained models

schedule le lundi 11 février 2019 de 17h00 à 18h00

Organisé par : G. Conchon-Kerjan, F. Coppini, B. Dembin

Intervenant : Ivailo Hartarsky (Paris Dauphine)
Lieu : Université Paris Diderot, Salle 1016 Bâtiment Sophie Germain

Sujet : Universality for critical kinetically constrained models

Résumé :
joint with Laure Marêché, Fabio Martinelli and Cristina Toninelli

 Kinetically constrained models (KCM) are reversible interacting particle systems on the Cartesian lattice with continuous time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the family of cellular automata with random initial state known as bootstrap percolation. KCM are of interest in their own right, owing to their use for modelling the liquid-glass transition. In two dimensions there are three classes of models with qualitatively different behaviour. Here we study in full generality the class termed `critical'. 

 We establish the universality partition of critical KCM and determine their critical exponent giving their expected infection time of the origin as well as spectral gap. We prove that there are two subclasses of critical models, one of which is governed by bootstrap percolation and shares its exponent. The other class exhibits exponential energy barriers, which double the bootstrap exponent for its KCM counterpart. The latter was conjectured by Martinelli, Morris and Toninelli, while the former disproves their conjecture.

In the talk we will concentrate on the bootstrap-dominated class and show that a peculiar purely combinatorial mechanism provides a very efficient means of moving infections.