  We investigate the dynamics of kinetically constrained models of glass
formers by analysing the statistics of trajectories of the dynamics, or
histories, using large deviation function methods. We show that, in general,
these models exhibit a first-order dynamical transition between active and
inactive dynamical phases. We argue that the dynamical heterogeneities
displayed by these systems are a manifestation of dynamical first-order phase
coexistence. In particular, we calculate dynamical large deviation functions,
both analytically and numerically, for the Fredrickson-Andersen model, the East
model, and constrained lattice gas models. We also show how large deviation
functions can be obtained from a Landau-like theory for dynamical fluctuations.
We discuss possibilities for similar dynamical phase-coexistence behaviour in
other systems with heterogeneous dynamics.
