{
  "id": "math/0505175",
  "version": "v2",
  "published": "2005-05-10T11:27:27.000Z",
  "updated": "2005-07-26T10:52:49.000Z",
  "title": "Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses",
  "authors": [
    "Radoslaw Adamczak"
  ],
  "comment": "Slightly enlarged and updated with respect to the previous version. Some misprints corrected",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove logarithmic Sobolev inequalities and concentration results for convex functions and a class of product random vectors. The results are used to derive tail and moment inequalities for chaos variables (in spirit of Talagrand and Arcones, Gine). We also show that the same proof may be used for chaoses generated by log-concave random variables, recovering results by Lochowski and present an application to exponential integrability of Rademacher chaos.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-07-26T10:52:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60B11"
    ],
    "keywords": [
      "logarithmic sobolev inequalities",
      "convex functions",
      "polynomial chaoses",
      "product random vectors",
      "log-concave random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5175A"
    }
  }
}