Bootstrap percolation and kinetically constrained spin models : critical time and lengths scales

Jeudi 18 mai 14:00-15:00 Cristina Toninelli - LPMA

Résumé : Recent years have seen a great deal of progress in understanding the behavior of bootstrap percolation models, a particular class of monotone cellular automata. In the two dimensional lattice there is now a quite satisfactory understanding of their evolution starting from a random initial condition, with a strikingly beautiful universality picture for their critical behavior.
Much less is known for their non-monotone stochastic counterpart, namely kinetically constrained models (KCM). In KCM each vertex is resampled (independently) at rate one by tossing a p-coin iff it can be infected in the next step by the bootstrap model. In particular infection can also heal, hence the non-monotonicity.
Besides the connection with bootstrap percolation, KCM have an interest in their own : when p->0 they display some of the most striking features of the liquid/glass transition, a major and still largely open problem in condensed matter physics.
In this talk I will discuss some recent results on the characteristic time scales of KCM as p → 0 and the connection with the critical behavior of the corresponding bootstrap models.

Bootstrap percolation and kinetically constrained spin models : critical time and lengths scales  Version PDF