On Mean Field Limits for Dynamical Systems
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© 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.
Published Version (Please cite this version)10.1007/s10955-015-1351-5
Publication InfoBoers, N; & Pickl, P (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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Visiting Professor in the Trinity College of Arts and Sciences
Starting with the autumn term 2018 I will teach the foundational mathematics and integrated science courses in the undergraduate program at DKU. In the coming years, other classes on several topics of mathematics and mathematical physics will be taught.