{
  "id": "1811.00353",
  "version": "v1",
  "published": "2018-11-01T13:13:33.000Z",
  "updated": "2018-11-01T13:13:33.000Z",
  "title": "Hanson-Wright inequality in Banach spaces",
  "authors": [
    "Radosław Adamczak",
    "Rafał Latała",
    "Rafał Meller"
  ],
  "categories": [
    "math.PR",
    "math.FA",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We discuss two-sided bounds for moments and tails of quadratic forms in Gaussian random variables with values in Banach spaces. We state a natural conjecture and show that it holds up to additional logarithmic factors. Moreover in a certain class of Banach spaces (including $L_r$-spaces) these logarithmic factors may be eliminated. As a corollary we derive upper bounds for tails and moments of quadratic forms in subgaussian random variables, which extend the Hanson-Wright inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-01T13:13:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60B11"
    ],
    "keywords": [
      "banach spaces",
      "hanson-wright inequality",
      "quadratic forms",
      "subgaussian random variables",
      "additional logarithmic factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}