{
  "id": "1712.09266",
  "version": "v1",
  "published": "2017-12-26T13:33:43.000Z",
  "updated": "2017-12-26T13:33:43.000Z",
  "title": "Geodesic of minimal length in the set of probability measures on graphs",
  "authors": [
    "Wilfrid Gangbo",
    "Wuchen Li",
    "Chenchen Mou"
  ],
  "comment": "31 Pages",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "We endow the set of probability measures on a weighted graph with a Monge--Kantorovich metric, induced by a function defined on the set of vertices. The graph is assumed to have $n$ vertices and so, the boundary of the probability simplex is an affine $(n-2)$--chain. Characterizing the geodesics of minimal length which may intersect the boundary, is a challenge we overcome even when the endpoints of the geodesics don't share the same connected components. It is our hope that this work would be a preamble to the theory of Mean Field Games on graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-26T13:33:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measures",
      "minimal length",
      "geodesics dont share",
      "mean field games",
      "probability simplex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}