{
  "id": "1601.03321",
  "version": "v1",
  "published": "2016-01-13T17:26:53.000Z",
  "updated": "2016-01-13T17:26:53.000Z",
  "title": "Scaling limits of discrete copulas are bridged Brownian sheets",
  "authors": [
    "Juliana Freire",
    "Nicolau C. Saldanha",
    "Carlos Tomei"
  ],
  "comment": "29 pages, 5 figures",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "For large $n$, take a random $n \\times n$ permutation matrix and its associated discrete copula $X_n$. For $a, b = 0, 1, \\ldots, n$, let $y_n(\\frac{a}{n},\\frac{b}{n}) = \\frac{1}{n} ( X_{a,b} - \\frac{ab}{n} )$; define $y_n: [0,1]^2 \\to R$ by interpolating quadratically on squares of side $\\frac{1}{n}$. We prove a Donsker type central limit theorem: $\\sqrt{n} y_n$ approaches a bridged Brownian sheet on the unit square.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-13T17:26:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60F05",
      "60J65",
      "60B20"
    ],
    "keywords": [
      "bridged brownian sheet",
      "scaling limits",
      "donsker type central limit theorem",
      "permutation matrix",
      "associated discrete copula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160103321F"
    }
  }
}