In this talk we will be interested in a one-dimensional exclusion process subject to strong kinetic constraints, which belongs to the class of cooperative kinetically constrained lattice gases. Its stochastic short range interaction exhibits a continuous phase transition to an absorbing state at a critical value of the particle density. Moreover its stationary states exhibit long range correlations. We will see that the macroscopic behavior of this microscopic dynamics, under periodic boundary conditions and diffusive time scaling, is ruled by a non-linear PDE belonging to free boundary problems. One of the ingredients is to show that the system typically reaches an ergodic component in subdiffusive time. Based on joint works with O. Blondel, C. Erignoux and M. Sasada
