{
  "id": "1408.1559",
  "version": "v2",
  "published": "2014-08-07T12:29:30.000Z",
  "updated": "2014-09-12T21:37:35.000Z",
  "title": "A Central Limit Theorem for the Length of the Longest Common Subsequence in Random Words",
  "authors": [
    "Christian Houdré",
    "Ümit Işlak"
  ],
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Let $(X_k)_{k \\geq 1}$ and $(Y_k)_{k\\geq1}$ be two independent sequences of independent identically distributed random variables having the same law and taking their values in a finite alphabet. Let $LC_n$ be the length of longest common subsequences in the two random words $X_1\\cdots X_n$ and $Y_1\\cdots Y_n$. Under assumptions on the distribution of $X_1$, $LC_n$ is shown to satisfy a central limit theorem. This is in contrast to the limiting distribution of the length of longest common subsequences in two independent uniform random permutations of $\\{1, \\dots, n\\}$, which is shown to be the Tracy-Widom distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-07T12:29:30.000Z",
      "abstract": "Let $(X_k)_{k \\geq 1}$ and $(Y_k)_{k\\geq1}$ be two independent sequences of independent identically distributed random variables having the same law and taking their values in a finite alphabet $\\mathcal{A}_m$. Let $LC_n$ be the length of the longest common subsequence of the random words $X_1\\cdots X_n$ and $Y_1\\cdots Y_n$. Under assumptions on the distribution of $X_1$, $LC_n$ is shown to satisfy a central limit theorem.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-12T21:37:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "60C05",
      "60F05"
    ],
    "keywords": [
      "longest common subsequence",
      "central limit theorem",
      "random words",
      "independent identically distributed random variables",
      "independent sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.1559H"
    }
  }
}