{
  "id": "1407.3639",
  "version": "v1",
  "published": "2014-07-14T13:23:52.000Z",
  "updated": "2014-07-14T13:23:52.000Z",
  "title": "Sampling Parts of Random Integer Partitions: A Probabilistic and Asymptotic Analysis",
  "authors": [
    "Ljuben Mutafchiev"
  ],
  "comment": "19 pages. arXiv admin note: substantial text overlap with arXiv:1306.6155",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\lambda$ be a partition of the positive integer $n$, selected uniformly at random among all such partitions. Corteel et al. (1999) proposed three different procedures of sampling parts of $\\lambda$ at random. They obtained limiting distributions of the multiplicity $\\mu_n=\\mu_n(\\lambda)$ of the randomly-chosen part as $n\\to\\infty$. The asymptotic behavior of the part size $\\sigma_n=\\sigma_n(\\lambda)$, under these sampling conditions, was found by Fristedt (1993) and Mutafchiev (2014). All these results motivated us to study the relationship between the size and the multiplicity of a randomly-selected part of a random partition. We describe it obtaining the joint limiting distributions of $(\\mu_n,\\sigma_n)$, as $n\\to\\infty$, for all these three sampling procedures. It turns out that different sampling plans lead to different limiting distributions for $(\\mu_n,\\sigma_n)$. Our results generalize those obtained earlier and confirm the known expressions for the marginal limiting distributions of $\\mu_n$ and $\\sigma_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-14T13:23:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "60C05",
      "60F05"
    ],
    "keywords": [
      "random integer partitions",
      "sampling parts",
      "asymptotic analysis",
      "probabilistic",
      "marginal limiting distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3639M"
    }
  }
}