Séminaire MODAL'X : Clément Erignoux (Laboratoire Paul Painlevé, Inria et Université de Lille)

Résumé : Kinetically Constrained Lattice Gases (KCLG) have been proposed as the conservative counterparts to Kinetically Constrained Models (KCM), and offer a range of toy models for phase transitions and interfaces progression. In this talk, I will describe a few examples of KCLGs and describe some of the mathematical challenges they offer. I will present recent results on their scaling limit in the diffusive scaling, that converges to a so-called two-phased Stefan problem (or Free boundary problem), as well as results on the evolution of their microscopic structure. I will also give some heuristic arguments to explain some of these results, and briefly present ongoing projects where we explore 2-dimensional analogous models.