{
  "id": "1012.2372",
  "version": "v2",
  "published": "2010-12-10T20:30:10.000Z",
  "updated": "2013-07-23T10:21:51.000Z",
  "title": "Singularity of Random Matrices over Finite Fields",
  "authors": [
    "Kenneth Maples"
  ],
  "comment": "16 pages, no figures",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Let $A$ be an $n \\times n$ random matrix with iid entries over a finite field of order $q$. Suppose that the entries do not take values in any additive coset of the field with probability greater than $1 - \\alpha$ for some fixed $0 < \\alpha < 1$. We show that the singularity probability converges to the uniform limit with an exponentially small error depending only on $\\alpha$. We also show that the distribution of the determinant of $A$ converges to its limiting distribution at an exponential rate.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-23T10:21:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "15B33",
      "60C05"
    ],
    "keywords": [
      "finite field",
      "random matrices",
      "singularity probability converges",
      "iid entries",
      "random matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.2372M"
    }
  }
}