Statistical properties of the gravitational force in a random
  homogeneous medium
  We discuss the statistical distribution of the gravitational (Newtonian)
force exerted on a test particle in a infinite random and homogeneous gas of
non-correlated particles. The exact solution is known as the Holtsmark
distribution at the limit of infinite system corresponding to the number of
particle N within the volume and the volume going to infinity. The statistical
behaviour of the gravitational force for scale comparable to the inter-distance
particle can be analyzed through the combination of the n-th nearest neighbor
particle contribution to the total gravitational force, which can be derived
from the joint probability density of location for a set of N particles. We
investigate two independent approaches to derive the joint probability density
of location for a set of N neighbors using integral forms and order statistics
to give a general expression of such probability distribution with generalised
dimension of space. We found that the non-finite dispersion of the Holtsmark
distribution is due to the single contribution of the first nearest neighbor in
the total gravitational force.
