{
  "id": "1907.10896",
  "version": "v1",
  "published": "2019-07-25T08:26:43.000Z",
  "updated": "2019-07-25T08:26:43.000Z",
  "title": "Log-Hessian formula and the Talagrand conjecture",
  "authors": [
    "N Gozlan",
    "Xue-Mei Li",
    "M Madiman",
    "C. Roberto",
    "P. -M Samson"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In 1989, Talagrand proposed a conjecture regarding the regularization effect on integrable functions of a natural Markov semigroup on the Boolean hypercube. While this conjecture remains unresolved, the analogous conjecture for the Ornstein-Uhlenbeck semigroup was recently resolved by Eldan-Lee and Lehec, by combining an inequality for the log-Hessian of this semigroup with a new deviation inequality for log-semiconvex functions under Gaussian measure. Our first goal is to explore the validity of both these ingredients for some diffusion semigroups in R n as well as for the M/M/$\\infty$ queue on the non-negative integers. Our second goal is to prove an analogue of Talagrand's conjecture for these settings, even in those cases where these ingredients are not valid.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-25T08:26:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "talagrand conjecture",
      "log-hessian formula",
      "natural markov semigroup",
      "talagrands conjecture",
      "regularization effect"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}