Mean nearest-neighbor distance in random packings of hard D-dimensional spheres

We derive the first nontrivial rigorous bounds on the mean distance between nearest neighbors in ergodic, isotropic packings of hard D-dimensional spheres that depend on the packing fraction and nearest-neighbor distribution function. Several interesting implications of these bounds for equilibrium as well as nonequilibrium ensembles are explored. For an equilibrium ensemble, we find accurate analytical approximations for for D=2 and 3 that apply up to random close packing. Our theoretical results are in excellent agreement with available computer-simulation data.