{
  "id": "math/0505692",
  "version": "v1",
  "published": "2005-05-31T19:05:05.000Z",
  "updated": "2005-05-31T19:05:05.000Z",
  "title": "Rank Independence and Rearrangements of Random Variables",
  "authors": [
    "Alexander Gnedin",
    "Zbigniew Nitecki"
  ],
  "comment": "29 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "A rearrangement of $n$ independent uniform $[0,1]$ random variables is a sequence of $n$ random variables $Y_1,...,Y_n$ whose vector of order statistics has the same distribution as that for the $n$ uniforms. We consider rearrangements satisfying the strong rank independence condition, that the rank of $Y_k$ among $Y_1,...,Y_k$ is independent of the values of $Y_1,...,Y_{k-1}$, for $k=1,...,n$. Nontrivial examples of such rearrangements are the travellers' processes defined by Gnedin and Krengel. We show that these are the only examples when $n=2$, and when certain restrictive assumptions hold for $n\\geq 3$; we also construct a new class of examples of such rearrangements for which the restrictive assumptions do not hold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-31T19:05:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "62G30"
    ],
    "keywords": [
      "random variables",
      "rearrangement",
      "strong rank independence condition",
      "order statistics",
      "nontrivial examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5692G"
    }
  }
}