Bootstrap percolation and interacting particle systems with kinetic constraints: critical time and length scales

Vortrag von Prof. Dr. Fabio Martinelli

Sprecher eingeladen von: Prof. Dr. Benjamin Schlein

Datum: 24.05.17  Zeit: 17.15 - 19.00  Raum: Y27H12

Recent years have seen a great deal of progress in understanding the behaviour 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 behaviour (length and time scales). Mu ch less is known for their non-monotone stochastic counterpart, namely kinetically constrained models (KCM). In a KCM the state of each vertex which could be infected by the bootstrap percolation rules is resampled (independently among the vertices) at rate one by tossing a p-coin. In particular infection can also heal, hence the non-monotonicity. Besides their connection with bootstrap percolation, KCMs have an strong interest in their own : as 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, after an introductory first part, I shall discuss (i) some recent conjectures relating the universality behaviour of critical KCMs to their bootstrap percolation counterpart and (ii) some very recent progresses towards proving the above conjectures. Joint project with C. Toninelli (Paris VII) and R. Morris (IMPA).