{
  "id": "1907.07900",
  "version": "v1",
  "published": "2019-07-18T06:51:06.000Z",
  "updated": "2019-07-18T06:51:06.000Z",
  "title": "Multi-marginal Entropy-Transport with repulsive cost",
  "authors": [
    "Augusto Gerolin",
    "Anna Kausamo",
    "Tapio Rajala"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.OC"
  ],
  "abstract": "In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the $\\Gamma$-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We also prove the entropy-regularized version of the Kantorovich duality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-18T06:51:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-marginal entropy-transport",
      "entropy-transport functional",
      "multi-marginal optimal transport problem",
      "study theoretical properties",
      "kantorovich duality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}