Gravitational force in weakly correlated particle spatial distributions

Area of Science:

• Astrophysics and Gravitational Physics
• Statistical Mechanics
• Computational Physics

Background:

• Gravitational force statistics are crucial for understanding large-scale structures in the universe.
• Chandrasekhar's work analyzed these statistics for purely Poisson point processes.
• Gauss-Poisson processes offer a more realistic model for particle distributions, incorporating correlations.

Purpose of the Study:

• To extend Chandrasekhar's analysis of gravitational force statistics to Gauss-Poisson point processes.
• To derive the asymptotic behavior of the probability density function of the gravitational force.
• To investigate the impact of density correlations on force statistics at different scales.

Main Methods:

• Analytical extension of Chandrasekhar's methods to Gauss-Poisson distributions.
• Derivation of the explicit asymptotic behavior for the force's probability density function.
• Numerical simulations of Gauss-Poisson processes to validate analytical approximations.

Main Results:

• A generalized Holtzmark statistics for gravitational force in weakly correlated particle distributions.
• Explicit formulas for the probability density function's behavior at large and small force values.
• Demonstration that small-scale density correlations significantly modify large-field force statistics.

Conclusions:

• The study provides a theoretical framework for gravitational force statistics in correlated systems.
• The findings offer insights into the influence of local density variations on global gravitational fields.
• Numerical validation confirms the accuracy of the extended analytical model for Gauss-Poisson processes.