Abstract
We show that the dynamics of kinetically constrained models of glass formerstakes place at a first-order coexistence line between active and inactivedynamical phases. We prove this by computing the large-deviation functions ofsuitable space-time observables, such as the number of configuration changes ina trajectory. We present analytic results for dynamic facilitated models in amean-field approximation, and numerical results for the Fredrickson-Andersenmodel, the East model, and constrained lattice gases, in various dimensions.This dynamical first-order transition is generic in kinetically constrainedmodels, and we expect it to be present in systems with fully jammed states.