# A probabilistic approach to the N-body problem [GA]

This work introduces a new interpretation of the gravitational N-body problem, based on the one-point probability density {\Psi} of finding a particle at a given loca- tion of phase space (x, v) at time t and the associated expected phase-space $\bar{f}$(x, v, t) = M {\Psi}(x, v, t), where M is the total mass of the system. At variance with the traditional paradigm, we consider that the problem is inherently stochastic, and therefore $\bar{f}$ corresponds to a weighted average over all possible random realisations of the initial conditions. In practice, we run several numerical experiments in one dimension where $\bar{f}$(x, v, t), and thus {\Psi}(x, v, t), are estimated from the average of a finite number S of independent simulations with N particles each. The proposed approach is extremely efficient from a computational point of view, with modest CPU and memory requirements, and it provides a very competitive alternative to traditional N-body simulations when the goal is to study the average properties of N-body systems, at the cost of abandoning the notion of well-defined trajectories for each individual particle.

M. Romero and Y. Ascasibar
Fri, 17 Mar 17
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