Bootstrap percolation and kinetically constrained models: universality results

par Cristina Toninelli (CNRS)

lundi 18 nov. 2024, 16:00 → 17:00 Europe/Paris

Fokko du Cloux (Braconnier)

Recent years have witnessed great progresses in the study of bootstrap percolation models (BP). On  the Euclidean lattice there is now a quite complete understanding of their evolution starting from a random initial condition, with a universality picture for their critical behavior.

In this seminar we will focus on their non-monotone stochastic counterpart, namely kinetically constrained models (KCM). Here each vertex is either infected or healthy and, iff it is infectable according to the BP rules,  its state is resampled (independently) at rate one to infected with probability p, and healthy with probability 1-p. 

I will discuss a series of results which establish the full universality picture of KCM in two dimensions. We will see  that, compared to those of BP, the universality classes for the stochastic dynamics are richer and the critical time scales diverge faster due to the dominant contribution of energy barriers. The seminar is based on joint works with

Ivailo Hartarsky, Laure Marêché, Fabio Martinelli, and Rob Morris.