{
  "id": "1409.8496",
  "version": "v1",
  "published": "2014-09-30T11:35:09.000Z",
  "updated": "2014-09-30T11:35:09.000Z",
  "title": "Gaussian Integrability of Distance Function under the Lyapunov Condition",
  "authors": [
    "Yuan Liu"
  ],
  "comment": "6 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note, we give a direct proof of the Gaussian integrability as $\\mu e^{\\delta d^2(x,x_0)} < \\infty$ for some $\\delta>0$ provided the Lyapunov condition for symmetric diffusion Markov operators, which answers a question proposed in Cattiaux-Guillin-Wu [3, Page 295]. The similar argument also works under the Gozlan's condition arising from [6, Proposition 3.5].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-30T11:35:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "60E15",
      "60J60"
    ],
    "keywords": [
      "gaussian integrability",
      "lyapunov condition",
      "distance function",
      "symmetric diffusion markov operators",
      "direct proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.8496L"
    }
  }
}