{
  "id": "1204.2517",
  "version": "v1",
  "published": "2012-04-11T18:31:41.000Z",
  "updated": "2012-04-11T18:31:41.000Z",
  "title": "Geodesics for a class of distances in the space of probability measures",
  "authors": [
    "Pierre Cardaliaguet",
    "Guillaume Carlier",
    "Bruno Nazaret"
  ],
  "categories": [
    "math.OC",
    "math.AP"
  ],
  "abstract": "In this paper, we study the characterization of geodesics for a class of distances between probability measures introduced by Dolbeault, Nazaret and Savar e. We first prove the existence of a potential function and then give necessary and suffi cient optimality conditions that take the form of a coupled system of PDEs somehow similar to the Mean-Field-Games system of Lasry and Lions. We also consider an equivalent formulation posed in a set of probability measures over curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-11T18:31:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measures",
      "suffi cient optimality conditions",
      "potential function",
      "mean-field-games system",
      "equivalent formulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2517C"
    }
  }
}