{
  "id": "0801.1221",
  "version": "v1",
  "published": "2008-01-08T12:49:33.000Z",
  "updated": "2008-01-08T12:49:33.000Z",
  "title": "On the singularity of random matrices with independent entries",
  "authors": [
    "Laurent Bruneau",
    "Francois Germinet"
  ],
  "comment": "to be published in the Proc. Amer. Math. Soc",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider n by n real matrices whose entries are non-degenerate random variables that are independent but non necessarily identically distributed, and show that the probability that such a matrix is singular is O(1/sqrt{n}). The purpose of this note is to provide a short and elementary proof of this fact using a Bernoulli decomposition of arbitrary non degenerate random variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-08T12:49:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52",
      "60C05"
    ],
    "keywords": [
      "random matrices",
      "independent entries",
      "arbitrary non degenerate random variables",
      "singularity",
      "non-degenerate random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}