We present a model of spheres moving in a high-dimensional compact spa
ce. We relate it to a mixed matrix model with a O(N) invariant model p
lus a P(N) invariant perturbation. We then study the low pressure regi
me by performing a diagrammatic expansion of this matrix model. Finall
y, we show the results from numerical simulations and we present evide
nce for a glassy regime at high pressures.