Cutoff for the Fredrickson-Andersen one spin facilitated model

The Fredrickson-Andersen one spin facilitated model belongs to the class of Kinetically Constrained Spin Models. It is a non attractive process with positive spectral gap. In this paper we give a precise result on the relaxation for this process on an interval [1, L] starting from any initial configuration. A consequence of this result is that this process exhibits cutoff at time L/(2v) with window O( √ L) for a certain positive constant v. The key ingredient is the study of the evolution of the leftmost empty site in a filled infinite half-line called the front. In the process of the proof, we improve recent results about the front motion by showing that it evolves at speed v according to a uniform central limit theorem.