{
  "id": "1506.02489",
  "version": "v1",
  "published": "2015-06-08T13:35:28.000Z",
  "updated": "2015-06-08T13:35:28.000Z",
  "title": "A new characterization of quadratic transportation-information inequalities",
  "authors": [
    "Yuan Liu"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "It is known that a quadratic transportation-information inequality $\\mathrm{W_2I}$ interpolates between the Talagrand's inequality $\\mathrm{W_2H}$ and the log-Sobolev inequality (LSI for short). Our aim of the present paper is threefold: (1) To prove $\\mathrm{W_2I}$ through the Lyapunov condition, which fills a gap in the subject of transport inequalities according to Cattiaux-Guillin-Wu [8]. (2) To prove the stability of $\\mathrm{W_2I}$ under bounded perturbations, which yields a transference principle in the sense of Holley-Stroock. (3) To prove $\\mathrm{W_2H}$ through a restricted $\\mathrm{W_2I}$, as a characterization of $\\mathrm{W_2H}$ similar to the restricted LSI according to Gozlan-Roberto-Samson [14].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-08T13:35:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic transportation-information inequality",
      "characterization",
      "log-sobolev inequality",
      "lyapunov condition",
      "transference principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150602489L"
    }
  }
}