A front evolution problem for the multidimensional East model

23.05.2022 15:15 – 17:15

In this talk we consider kinetically constrained models (KCM). KCM are Markov processes that model core properties of the liquid-glass transition. Mathematically they are the continuous time generalisation with recovery of bootstrap percolation. In particular, we consider a natural front evolution problem (or alternatively: an infection spreading velocity problem) for the East process on Z^d, d ≥ 2, a well studied directed KCM. Shape theorems in dimension d ≥ 2 have been notoriously hard to prove for KCM due to the lack of attractiveness. In this talk we show first bounds giving that the front of the East model is extremely elongated in Z^d as the equilibrium probability of facilitating vertices vanishes. Together with the board outlines of the proof we give qualitative reasons for this
supported by simulations. These results allow finding a set behind the front that tends to equilibrium and a cutoff of the mixing time on the d-dimensional cube.

Lieu

Salle 1-15, Séminaire "Mathématique physique"

entrée libre