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- Title
Propagation of chaos for the Vlasov-Poisson-Fokker-Planck system in 1D.
- Authors
Hauray, Maxime; Salem, Samir
- Abstract
We consider a particle system in 1D, interacting via repulsive or attractive Coulomb forces. We prove the trajectorial propagation of molecular chaos towards a nonlinear SDE associated to the Vlasov-Poisson-Fokker-Planck equation. We obtain a quantitative estimate of convergence in the mean in MKW metric of order one, with an optimal convergence rate of order N−1/2. We also prove some exponential concentration inequalities of the associated empirical measures. A key argument is a weak-strong stability estimate on the (nonlinear) VPFP equation, that we are able to adapt for the particle system in some sense.
- Subjects
CHAOS theory; STOCHASTIC differential equations; STOCHASTIC convergence; UNIQUENESS (Mathematics); BROWNIAN motion
- Publication
Kinetic & Related Models, 2019, Vol 12, Issue 2, p269
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2019012