{
  "id": "0704.0876",
  "version": "v1",
  "published": "2007-04-06T11:15:47.000Z",
  "updated": "2007-04-06T11:15:47.000Z",
  "title": "Non-monotone convergence in the quadratic Wasserstein distance",
  "authors": [
    "Walter Schachermayer",
    "Uwe Schmock",
    "Josef Teichmann"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We give an easy counter-example to Problem 7.20 from C. Villani's book on mass transport: in general, the quadratic Wasserstein distance between $n$-fold normalized convolutions of two given measures fails to decrease monotonically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-06T11:15:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B10"
    ],
    "keywords": [
      "quadratic wasserstein distance",
      "non-monotone convergence",
      "villanis book",
      "mass transport",
      "fold normalized convolutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.0876S"
    }
  }
}