Mixing time and local exponential ergodicity of the East-like process in Zd

The East process, a well known reversible linear chain of spins, represents the prototype of a general class of interacting particle sys- tems with constraints modeling the dynamics of real glasses. In this paper we consider a generalization of the East process living in the d-dimensional lattice and we establish new progresses on the out-of-equilibrium behav- ior. Despite the fact that convergence to the stationary reversible measure in the uniform norm cannot hold because of the presence of blocked con- figurations, we prove a form of (local) exponential ergodicity when the initial distribution is different from the stationary one. We also establish that the mixing time in a finite box grows linearly in the side of the box.