{
  "id": "1611.04960",
  "version": "v1",
  "published": "2016-11-15T17:45:12.000Z",
  "updated": "2016-11-15T17:45:12.000Z",
  "title": "A PDE approach to a 2-dimensional matching problem",
  "authors": [
    "Luigi Ambrosio",
    "Federico Stra",
    "Dario Trevisan"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square. Our technique is based on a rigorous formulation of the challenging PDE ansatz by S.\\ Caracciolo et al.\\ (Phys. Rev. E, {\\bf 90} 012118, 2014) that \"linearise\" the Monge-Amp\\`ere equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-15T17:45:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "49J55",
      "60H15"
    ],
    "keywords": [
      "pde approach",
      "independent uniform random variables",
      "expected quadratic transportation cost",
      "asymptotic results",
      "random matching problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}