Universality in dimension 1 of kinetically constrained lattice gases

Abstract: Kinetically constrained lattice gases are interacting particle systems with conserved number of particles, having degenerate rates caused by a kinetic constraint. Over the past decade, there has been major progress in the study of their non-conservative counterpart, kinetically constrained spin models: in dimensions 1 and 2, we have a good understanding of the universality classes of these models. However, the conservative systems are much more challenging to analyze, and very few results are available. The purpose of this paper is to describe universality in the one dimensional case. We will characterize the three universality classes, determining whether such a model is always ergodic, never ergodic, or exhibits an ergodicity phase transition.