{
  "id": "1902.03476",
  "version": "v1",
  "published": "2019-02-09T19:12:24.000Z",
  "updated": "2019-02-09T19:12:24.000Z",
  "title": "On the error bound in the normal approximation for Jack measures",
  "authors": [
    "Louis H. Y. Chen",
    "Lê Văn Thành"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we obtain uniform and non-uniform bounds on the Kolmogorov distance in the normal approximation for Jack deformations of the character ratio, by using Stein's method and zero-bias couplings. Our uniform bound comes very close to that conjectured by Fulman [J. Combin. Theory Ser. A, 108 (2004), 275--296]. As a by-product of the proof of the non-uniform bound, we obtain a Rosenthal-type inequality for zero-bias couplings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-09T19:12:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normal approximation",
      "jack measures",
      "error bound",
      "non-uniform bound",
      "zero-bias couplings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}