{
  "id": "1407.1157",
  "version": "v1",
  "published": "2014-07-04T09:08:58.000Z",
  "updated": "2014-07-04T09:08:58.000Z",
  "title": "On the rate of convergence of empirical measures in $\\infty$-transportation distance",
  "authors": [
    "Nicolás García Trillos",
    "Dejan Slepčev"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is optimal in terms of scaling with the number of sample points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-04T09:08:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B10",
      "60D05",
      "05C70"
    ],
    "keywords": [
      "transportation distance",
      "empirical measure",
      "convergence",
      "sample points",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.1157G"
    }
  }
}