On Mean Field Limits for Dynamical Systems
dc.contributor.author | Boers, N | |
dc.contributor.author | Pickl, P | |
dc.date.accessioned | 2018-06-04T15:40:40Z | |
dc.date.available | 2018-06-04T15:40:40Z | |
dc.date.issued | 2016-07 | |
dc.date.updated | 2018-06-04T15:40:39Z | |
dc.description.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. | |
dc.identifier.issn | 0022-4715 | |
dc.identifier.issn | 1572-9613 | |
dc.identifier.uri | ||
dc.publisher | Springer Science and Business Media LLC | |
dc.relation.ispartof | Journal of Statistical Physics | |
dc.relation.isversionof | 10.1007/s10955-015-1351-5 | |
dc.subject | Vlasov equation | |
dc.subject | Classical mean-field | |
dc.subject | Statisitcal mechanics | |
dc.subject | Propagation of chaos | |
dc.title | On Mean Field Limits for Dynamical Systems | |
dc.type | Journal article | |
pubs.issue | 1 | |
pubs.organisational-group | Duke Kunshan University | |
pubs.organisational-group | Duke | |
pubs.organisational-group | Duke Kunshan University Faculty | |
pubs.publication-status | Published | |
pubs.volume | 164 |