Boers, Niklas; Pickl, Peter
(2016):
On Mean Field Limits for Dynamical Systems.
In: Journal of Statistical Physics, Vol. 164, No. 1: pp. 116

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Abstract
We present a purely probabilistic proof of propagation of molecular chaos for Nparticle systems in dimension 3 with interaction forces scaling like with smaller but close to one and cutoff at . The proof yields a Gronwall estimate for the maximal distance between exact microscopic and approximate meanfield dynamics. This can be used to show weak convergence of the oneparticle marginals to solutions of the respective meanfield equation without cutoff in a quantitative way. Our results thus lead to a derivation of the Vlasov equation from the microscopic Nparticle dynamics with force term arbitrarily close to the physically relevant Coulomb and gravitational forces.