11h - Colloquium: Cristina Toninelli (Ceremade, Université Paris Dauphine)

 

Recent years have witnessed great progresses in the study of bootstrap percolation models (BP). 

In the initial configuration sites are occupied with probability p. The evolution of BP occurs at discrete times: empty sites stay empty and occupied sites are emptied iff a certain model dependent neighborhood is already empty.  On Z^d there is now a quite complete understanding of their evolution starting from a random initial condition, with a universality picture for their critical behavior.

Much less is known for 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.  These models, which have been introduced and intensively investigated in physics literature as toy models for the liquid/glass transitions, pose very challenging and interesting mathematical problems. In fact, the presence of the constraints induce non-attractiveness, the occurrence of several invariant measures, and the failure of many powerful tools (coercive inequalities, coupling, censoring) to analyze relaxation to equilibrium.

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 I.Hartarsky, L.Marêché, F.Martinelli, and R.Morris.