{
  "id": "math/0407016",
  "version": "v1",
  "published": "2004-07-01T19:02:58.000Z",
  "updated": "2004-07-01T19:02:58.000Z",
  "title": "Limit law of the standard right factor of a random Lyndon word",
  "authors": [
    "Regine Marchand",
    "Elahe Zohoorian Azad"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider the set of finite words on a totally ordered alphabet with $q$ letters. We prove that the distribution of the length of the standard right factor of a random Lyndon word with length $n$, divided by $n$, converges to: $$\\mu(dx)=\\frac1q \\delta_{1}(dx) + \\frac{q-1}q \\mathbf{1}_{[0,1)}(x)dx,$$ when $n$ goes to infinity. The convergence of all moments follows. This paper completes thus the results of \\cite{Bassino}, giving the asymptotics of the mean length of the standard right factor of a random Lyndon word with length $n$ in the case of a two letters alphabet.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-07-01T19:02:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "standard right factor",
      "random lyndon word",
      "limit law",
      "paper completes",
      "finite words"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7016M"
    }
  }
}