{
  "id": "1001.1167",
  "version": "v2",
  "published": "2010-01-07T21:11:03.000Z",
  "updated": "2010-11-24T19:44:51.000Z",
  "title": "A simple reduction from a biased measure on the discrete cube to the uniform measure",
  "authors": [
    "Nathan Keller"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We show that certain statements related to the Fourier-Walsh expansion of functions with respect to a biased measure on the discrete cube can be deduced from the respective results for the uniform measure by a simple reduction. In particular, we present simple generalizations to the biased measure $\\mu_p$ of the Bonami-Beckner hypercontractive inequality, and of Talagrand's lower bound on the size of the boundary of subsets of the discrete cube. Our generalizations are tight up to constant factors.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-24T19:44:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D40",
      "60C05",
      "06E30"
    ],
    "keywords": [
      "discrete cube",
      "biased measure",
      "uniform measure",
      "simple reduction",
      "talagrands lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.1167K"
    }
  }
}