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arXiv:1510.06260 [math.AP]AbstractReferencesReviewsResources

Propagation of chaos for the Vlasov-Poisson-Fokker-Planck system in 1D

Maxime Hauray, Samir Salem

Published 2015-10-21Version 1

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 expectation, 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.

Comments: 30 p
Categories: math.AP, math.PR
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