FREDRICKSON-ANDERSEN ONE SPIN FACILITATED MODEL OUT OF EQUILIBRIUM

WeconsidertheFredrickson-Andersenonespinfacilitatedmodel (FA1f) on an infinite connected graph with polynomial growth. Each site with rate one refreshes its occupation variable to a filled or to an empty state with probability p ∈ [0, 1] or q = 1 − p respectively, provided that at least one of its nearest neighbours is empty. We study what happens when the evolution does not start from the equilibrium p-Bernoulli mea- sure μ and prove convergence to equilibrium when the vacancy density q is above a proper threshold q ̄ < 1. The convergence is exponential or stretched exponential, depending on the growth of the graph. In particu- lar it is exponential on Zd for d = 1 and stretched exponential for d > 1. The above result holds when the starting measure ν is such that the mean distance between two nearest empty sites is uniformly bounded. Our re- sult can be generalized to other non cooperative models.