{
  "id": "1806.07669",
  "version": "v1",
  "published": "2018-06-20T11:30:44.000Z",
  "updated": "2018-06-20T11:30:44.000Z",
  "title": "The Infinite Limit of Random Permutations Avoiding Patterns of Length Three",
  "authors": [
    "Ross G. Pinsky"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "For $\\tau\\in S_3$, let $\\mu_n^{\\tau}$ denote the uniformly random probability measure on the set of $\\tau$-avoiding permutations in $S_n$. Let $\\mathbb{N}^*=\\mathbb{N}\\cup\\{\\infty\\}$ with an appropriate metric and denote by $S(\\mathbb{N},\\mathbb{N}^*)$ the compact metric space consisting of functions $\\sigma=\\{\\sigma_i\\}_{ i=1}^\\infty$ from $\\mathbb{N}$ to $\\mathbb{N}^*$ which are injections when restricted to $\\sigma^{-1}(\\mathbb{N})$\\rm; that is, if $\\sigma_i=\\sigma_j$, $i\\neq j$, then $\\sigma_i=\\infty$. Extending permutations $\\sigma\\in S_n$ by defining $\\sigma_j=j$, for $j>n$, we have $S_n\\subset S(\\mathbb{N},\\mathbb{N}^*)$. For each $\\tau\\in S_3$, we study the limiting behavior of the measures $\\{\\mu_n^{\\tau}\\}_{n=1}^\\infty$ on $S(\\mathbb{N},\\mathbb{N}^*)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-20T11:30:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60B10",
      "05A05"
    ],
    "keywords": [
      "random permutations avoiding patterns",
      "infinite limit",
      "uniformly random probability measure",
      "compact metric space consisting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}