{
  "id": "2107.03616",
  "version": "v1",
  "published": "2021-07-08T05:36:11.000Z",
  "updated": "2021-07-08T05:36:11.000Z",
  "title": "Scaling Limit of Moderately Interacting Particle Systems with Singular Interaction and Environmental Noise",
  "authors": [
    "Shuchen Guo",
    "Dejun Luo"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider moderately interacting particle systems with singular interaction kernel and environmental noise. It is shown that the mollified empirical measures converge in strong norms to the unique (local) solutions of nonlinear Fokker-Planck equations. The approach works for the Biot-Savart and Poisson kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-08T05:36:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moderately interacting particle systems",
      "environmental noise",
      "scaling limit",
      "nonlinear fokker-planck equations",
      "singular interaction kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}