{
  "id": "1306.2872",
  "version": "v3",
  "published": "2013-06-12T15:54:52.000Z",
  "updated": "2013-10-01T17:09:19.000Z",
  "title": "Hanson-Wright inequality and sub-gaussian concentration",
  "authors": [
    "Mark Rudelson",
    "Roman Vershynin"
  ],
  "comment": "10 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matrices.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-01T17:09:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hanson-wright inequality",
      "sub-gaussian concentration",
      "sub-gaussian random variables",
      "sub-gaussian random vectors",
      "quadratic forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.2872R"
    }
  }
}