{
  "id": "1601.08098",
  "version": "v1",
  "published": "2016-01-29T13:30:17.000Z",
  "updated": "2016-01-29T13:30:17.000Z",
  "title": "Gradient flow structure for McKean-Vlasov equations on discrete spaces",
  "authors": [
    "Matthias Erbar",
    "Max Fathi",
    "Vaios Laschos",
    "André Schlichting"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work, we show that a family of non-linear mean-field equations on discrete spaces, can be viewed as a gradient flow of a natural free energy functional with respect to a certain metric structure we make explicit. We also prove that this gradient flow structure arises as the limit of the gradient flow structures of a natural sequence of N-particle dynamics, as N goes to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-29T13:30:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete spaces",
      "mckean-vlasov equations",
      "natural free energy functional",
      "gradient flow structure arises",
      "non-linear mean-field equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160108098E"
    }
  }
}