{
  "id": "1504.01689",
  "version": "v1",
  "published": "2015-04-07T18:01:23.000Z",
  "updated": "2015-04-07T18:01:23.000Z",
  "title": "Invariance principle on the slice",
  "authors": [
    "Yuval Filmus",
    "Guy Kindler",
    "Elchanan Mossel",
    "Karl Wimmer"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We prove an invariance principle for functions on a slice of the Boolean cube, which is the set of all vectors {0,1}^n with Hamming weight k. Our invariance principle shows that a low-degree, low-influence function has similar distributions on the slice, on the entire Boolean cube, and on Gaussian space. Our proof relies on a combination of ideas from analysis and probability, algebra and combinatorics. Our result imply a version of majority is stablest for functions on the slice, a version of Bourgain's tail bound, and a version of the Kindler-Safra theorem. As a corollary of the Kindler-Safra theorem, we prove a stability result of Wilson's theorem for t-intersecting families of sets, improving on a result of Friedgut.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-07T18:01:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariance principle",
      "kindler-safra theorem",
      "entire boolean cube",
      "bourgains tail bound",
      "proof relies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150401689F"
    }
  }
}