{
  "id": "1801.05577",
  "version": "v1",
  "published": "2018-01-17T07:42:48.000Z",
  "updated": "2018-01-17T07:42:48.000Z",
  "title": "The rank of random regular digraphs of constant degree",
  "authors": [
    "Alexander Litvak",
    "Anna Lytova",
    "Konstantin Tikhomirov",
    "Nicole Tomczak-Jaegermann",
    "Pierre Youssef"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $d$ be a fixed large integer. For any $n$ larger than $d$, let $A_n$ be the adjacency matrix of the random directed $d$-regular graph on $n$ vertices, with the uniform distribution. We show that $A_n$ has rank at least $n-1$ with probability going to one as $n$ goes to infinity. The proof combines the method of simple switchings and a recent result of the authors on delocalization of eigenvectors of $A_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-17T07:42:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52",
      "46B06",
      "05C80"
    ],
    "keywords": [
      "random regular digraphs",
      "constant degree",
      "fixed large integer",
      "adjacency matrix",
      "regular graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}