Large deviations and heterogeneities in driven or non-driven glassy systems

We give a short overview of the results for large deviations of dynamical quantities obtained for models of glassy systems. We introduce the paper with the study of kinetically constrained models (KCMs), first without external forcing. In these models, it has been shown using the thermodynamic formalism for histories, that there is a coexistence between an active and an inactive phase. Later, it has been found that adding a driving field to a KCM model leads to a singularity in the large deviation function of the current at large fields. Finally we report on recent studies on realistic glassy systems, and open directions for future research