{
  "id": "math/0411095",
  "version": "v5",
  "published": "2004-11-04T17:02:11.000Z",
  "updated": "2008-06-30T21:10:56.000Z",
  "title": "On random $\\pm 1$ matrices: Singularity and Determinant",
  "authors": [
    "Terence Tao",
    "Van Vu"
  ],
  "comment": "25 pages, no figures. Slight numerical corrections to Lemma 2.2",
  "journal": "Random Structures and Algorithms 28 (2006), 1-23",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "This papers contains two results concerning random $n \\times n$ Bernoulli matrices. First, we show that with probability tending to one the determinant has absolute value $\\sqrt {n!} \\exp(O(\\sqrt(n log n)))$. Next, we prove a new upper bound $.939^n$ on the probability that the matrix is singular. We also give some generalizations to other random matrix models.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2008-06-30T21:10:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52"
    ],
    "keywords": [
      "determinant",
      "singularity",
      "random matrix models",
      "papers contains",
      "probability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11095T"
    }
  }
}