Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems

We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time) rather than in configuration space. To illustrate our general ideas, we analyze the one dimensional (d=1) Fredrickson-Andersen and East models. Dynamics of such dynamically constrained systems are shown to be isomorphic to the statics of d+1 dimensional dense mixtures of polydisperse non-interpenetrating domains. The domains coincide with arrested regions in trajectory space.