A mean-field hard-spheres model of glass

We present a model of spheres moving in a high-dimensional compact space. We relate it to a mixed matrix model with a O(N) invariant model plus a P(N) invariant perturbation. We then study the low pressure regime by performing a diagrammatic expansion of this matrix model. Finally, we show the results from numerical simulations and we present evidence for a glassy regime at high pressures.