On Mean Field Limits for Dynamical Systems

Published

Journal Article

© 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| 3λ-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.

Full Text

Cited Authors

  • Boers, N; Pickl, P

Published Date

  • July 1, 2016

Published In

Volume / Issue

  • 164 / 1

International Standard Serial Number (ISSN)

  • 0022-4715

Digital Object Identifier (DOI)

  • 10.1007/s10955-015-1351-5

Citation Source

  • Scopus