{
  "id": "2105.11384",
  "version": "v1",
  "published": "2021-05-24T16:21:56.000Z",
  "updated": "2021-05-24T16:21:56.000Z",
  "title": "The singularity probability of a random symmetric matrix is exponentially small",
  "authors": [
    "Marcelo Campos",
    "Matthew Jenssen",
    "Marcus Michelen",
    "Julian Sahasrabudhe"
  ],
  "comment": "48 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Let $A$ be drawn uniformly at random from the set of all $n\\times n$ symmetric matrices with entries in $\\{-1,1\\}$. We show that \\[ \\mathbb{P}( \\det(A) = 0 ) \\leq e^{-cn},\\] where $c>0$ is an absolute constant, thereby resolving a well-known conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-24T16:21:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random symmetric matrix",
      "singularity probability",
      "exponentially small",
      "absolute constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}