{
  "id": "1312.2382",
  "version": "v1",
  "published": "2013-12-09T11:12:23.000Z",
  "updated": "2013-12-09T11:12:23.000Z",
  "title": "Bridges and random truncations of random matrices",
  "authors": [
    "Vincent Beffara",
    "Catherine Donati-Martin",
    "Alain Rouault"
  ],
  "comment": "This paper has the same purpose as arXiv:1302.6539v1 from the second and third-named authors, but the method of proof is drastically different since now we use the results of arXiv:1007.1366v4 and a subordination",
  "categories": [
    "math.PR"
  ],
  "abstract": "We continue to study the squared Frobenius norm of a submatrix of a $n \\times n$ random unitary matrix. When the choice of the submatrix is deterministic and its size is $[ns] \\times [nt]$, we proved in a previous paper that, after centering and without any rescaling, the two-parameter process converges in distribution to a bivariate Brownian bridge. Here, we consider Bernoulli independent choices of rows and columns with respective parameters $s$ and $t$. We prove by subordination that after centering and rescaling by $n^{-1/2}$, the process converges to another Gaussian process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-09T11:12:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "60F17",
      "60J65"
    ],
    "keywords": [
      "random matrices",
      "random truncations",
      "bivariate brownian bridge",
      "bernoulli independent choices",
      "two-parameter process converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.2382B"
    }
  }
}