  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.
