{
  "id": "math/0407139",
  "version": "v1",
  "published": "2004-07-08T14:36:45.000Z",
  "updated": "2004-07-08T14:36:45.000Z",
  "title": "Concentration of permanent estimators for certain large matrices",
  "authors": [
    "Shmuel Friedland",
    "Brian Rider",
    "Ofer Zeitouni"
  ],
  "journal": "Annals of Probability 2004, Vol. 14, No. 3, 1559-1576",
  "doi": "10.1214/105051604000000396",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let A_n=(a_{ij})_{i,j=1}^n be an n\\times n positive matrix with entries in [a,b], 0<a\\le b. Let X_n=(\\sqrta_{ij}x_{ij})_{i,j=1}^n be a random matrix, where {x_{ij}} are i.i.d. N(0,1) random variables. We show that for large n, \\det (X_n^TX_n) concentrates sharply at the permanent of A_n, in the sense that n^{-1}\\log (\\det(X_n^TX_n)/perA_n)\\to_{n\\to\\infty}0 in probability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-07-08T14:36:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52"
    ],
    "keywords": [
      "permanent estimators",
      "large matrices",
      "concentration",
      "random variables"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7139F"
    }
  }
}