{
  "id": "1904.08211",
  "version": "v1",
  "published": "2019-04-17T12:02:33.000Z",
  "updated": "2019-04-17T12:02:33.000Z",
  "title": "Restricted hypercontractivity on the Poisson space",
  "authors": [
    "Ivan Nourdin",
    "Giovanni Peccati",
    "Xiaochuan Yang"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that the Ornstein-Uhlenbeck semigroup associated with a general Poisson random measure is hypercontractive, whenever it is restricted to non-increasing mappings on configuration spaces. We deduce from this result some versions of Talagrand's $L^1$-$L^2$ inequality for increasing and concave mappings, and we build examples showing that such an estimate represents a strict improvement of the classical Poincar\\'e inequality. We complement our finding with several results of independent interest, such as gradient estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-17T12:02:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "poisson space",
      "restricted hypercontractivity",
      "general poisson random measure",
      "classical poincare inequality",
      "gradient estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}