On Mean Field Limits for Dynamical Systems

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2016-07

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Abstract

© 2015, Springer Science+Business Media New York. We present a purely probabilistic proof of propagation of molecular chaos for N-particle systems in dimension 3 with interaction forces scaling like 1 / | q| 3 λ - 1 with λ smaller but close to one and cut-off at q= N - 1 / 3 . The proof yields a Gronwall estimate for the maximal distance between exact microscopic and approximate mean-field dynamics. This can be used to show weak convergence of the one-particle marginals to solutions of the respective mean-field equation without cut-off in a quantitative way. Our results thus lead to a derivation of the Vlasov equation from the microscopic N-particle dynamics with force term arbitrarily close to the physically relevant Coulomb- and gravitational forces.

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10.1007/s10955-015-1351-5

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Boers, N, and P Pickl (2016). On Mean Field Limits for Dynamical Systems. Journal of Statistical Physics, 164(1). 10.1007/s10955-015-1351-5 Retrieved from https://hdl.handle.net/10161/17109.

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