%0 Unpublished work
%T Propagation of chaos for the Vlasov-Poisson-Fokker-Planck system in 1D
%+ Institut de Mathématiques de Marseille (I2M)
%A Hauray, Maxime
%A Salem, Samir
%Z 30 p, with respect to v1: some typos corrected and a more precise theorem of propagation of chaos
%Z I2M:15-140
%8 2015-11-13
%D 2015
%Z 1510.06260
%Z Mathematics [math]/Analysis of PDEs [math.AP]
%Z Mathematics [math]/Probability [math.PR]Preprints, Working Papers, ...
%X 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.
%G English
%L hal-01257016
%U https://hal.science/hal-01257016
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-
%~ TDS-MACS