On Mean Field Limits for Dynamical Systems

Boers, Niklas and Pickl, Peter (2016): On Mean Field Limits for Dynamical Systems. In: Journal of Statistical Physics, Vol. 164, No. 1: pp. 1-16

Abstract

We present a purely probabilistic proof of propagation of molecular chaos for N-particle systems in dimension 3 with interaction forces scaling like with smaller but close to one and cut-off at . 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0022-4715
• Language: English