  We investigate the distribution of the volume and coordination number
associated to each particle in a jammed packing of monodisperse hard sphere
using the mesoscopic ensemble developed in Nature 453, 606 (2008). Theory
predicts an exponential distribution of the orientational volumes for random
close packings and random loose packings. A comparison with computer generated
packings reveals deviations from the theoretical prediction in the volume
distribution, which can be better modeled by a compressed exponential function.
On the other hand, the average of the volumes is well reproduced by the theory
leading to good predictions of the limiting densities of RCP and RLP. We
discuss a more exact theory to capture the volume distribution in its entire
range. The available data suggests a plausible order/disorder transition
defining random close packings. Finally, we consider an extended ensemble to
calculate the coordination number distribution which is shown to be of an
exponential and inverse exponential form for coordinations larger and smaller
than the average, respectively, in reasonable agreement with the simulated
data.
