Gravitational force in weakly correlated particle spatial distributions

The statistics of gravitational or Newtonian force was studied in a class of weakly correlated spatial distributions of pointlike and unitary mass of particles generated by the Gauss-Poisson point process. The features of the analysis introduced by Chandrasekhar for purely Poisson processes was presented. The asymptotic behavior of the probability density function of the force for both large and small values of the field was presented as a generalization of the Holtzmark statistics. It was shown how the modifications depended on the density correlations introduced at small scales.