{
  "id": "1206.5931",
  "version": "v1",
  "published": "2012-06-26T09:20:39.000Z",
  "updated": "2012-06-26T09:20:39.000Z",
  "title": "Equivalence of the Poincaré inequality with a transport-chi-square inequality in dimension one",
  "authors": [
    "Benjamin Jourdain"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we prove that, in dimension one, the Poincar\\'e inequality is equivalent to a new transport-chi-square inequality linking the square of the quadratic Wasserstein distance with the chi-square pseudo-distance. We also check tensorization of this transport-chi-square inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-26T09:20:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivalence",
      "quadratic wasserstein distance",
      "poincare inequality",
      "chi-square pseudo-distance",
      "check tensorization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.5931J"
    }
  }
}