{
  "id": "1510.06260",
  "version": "v1",
  "published": "2015-10-21T14:12:57.000Z",
  "updated": "2015-10-21T14:12:57.000Z",
  "title": "Propagation of chaos for the Vlasov-Poisson-Fokker-Planck system in 1D",
  "authors": [
    "Maxime Hauray",
    "Samir Salem"
  ],
  "comment": "30 p",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-21T14:12:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vlasov-poisson-fokker-planck system",
      "propagation",
      "particle system",
      "optimal convergence rate",
      "exponential concentration inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151006260H"
    }
  }
}