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

Maxime Hauray; Samir Salem

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arXiv · 1510.06260

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

Maxime Hauray·Samir Salem

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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 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.

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Maxime Hauray, Samir Salem. 2015-10-21. Propagation of chaos for the Vlasov-Poisson-Fokker-Planck system in 1D. https://arxiv.org/abs/1510.06260

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