{
  "id": "1402.3438",
  "version": "v1",
  "published": "2014-02-14T11:20:30.000Z",
  "updated": "2014-02-14T11:20:30.000Z",
  "title": "$W_{1,+}$-interpolation of probability measures on graphs",
  "authors": [
    "Erwan Hillion"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We generalize an equation introduced by Benamou and Brenier, characterizing Wasserstein W_p-geodesics for p > 1, from the continuous setting of probability distributions on a Riemannian manifold to the discrete setting of probability distributions on a general graph. Given an initial and a final distributions f_0 and f_1, we prove the existence of a curve (f_t) satisfying this Benamou-Brenier equation. We also show that such a curve can be described as a mixture of binomial distributions with respect to a coupling that is solution of a certain optimization problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-14T11:20:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measures",
      "interpolation",
      "probability distributions",
      "benamou-brenier equation",
      "general graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.3438H"
    }
  }
}