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

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1572-9613

dc.identifier.uri

https://hdl.handle.net/10161/17109

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

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Classical mean-field

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Statisitcal mechanics

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Propagation of chaos

dc.title

On Mean Field Limits for Dynamical Systems

dc.type

Journal article

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1

pubs.organisational-group

Duke Kunshan University

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Duke

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Duke Kunshan University Faculty

pubs.publication-status

Published

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164

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