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Updated: Aug 17, 2026

Spatial Separation of Molecular Conformers and Clusters
Published on: January 9, 2014
Gravitational force in weakly correlated particle spatial distributions
Andrea Gabrielli1, Adolfo Paolo Masucci, Francesco Sylos Labini
1E Fermi" Studies and Research Center, Via Panisperna 89 A, Compendio del Viminale, 00184 Rome, Italy.
Abstract:
We study the statistics of the gravitational (Newtonian) force in a particular class of weakly correlated spatial distributions of pointlike and unitary mass particles generated by the so-called Gauss-Poisson point processes. In particular we extend to these distributions the analysis that Chandrasekhar introduced for purely Poisson processes. In this way we can find the explicit asymptotic behavior of the probability density function of the force for both large and small values of the field as a generalization of the Holtzmark statistics. In particular, we show how the modifications at large fields depend on the density correlations introduced at small scales. The validity of the introduced approximations is positively tested through a direct comparison with the analysis of the statistics of the gravitational force in numerical simulations of Gauss-Poisson processes.
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