{
  "id": "1801.08934",
  "version": "v1",
  "published": "2018-01-26T18:56:13.000Z",
  "updated": "2018-01-26T18:56:13.000Z",
  "title": "Limit theorems for the least common multiple of a random set of integers",
  "authors": [
    "Gerold Alsmeyer",
    "Zakhar Kabluchko",
    "Alexander Marynych"
  ],
  "comment": "19 pages, 2 figures",
  "categories": [
    "math.PR",
    "math.NT"
  ],
  "abstract": "Let $L_{n}$ be the least common multiple of a random set of integers obtained from $\\{1,\\ldots,n\\}$ by retaining each element with probability $\\theta\\in (0,1)$ independently of the others. We prove that the process $(\\log L_{\\lfloor nt\\rfloor})_{t\\in [0,1]}$, after centering and normalization, converges weakly to a certain Gaussian process that is not Brownian motion. Further results include a strong law of large numbers for $\\log L_{n}$ as well as Poisson limit theorems in regimes when $\\theta$ depends on $n$ in an appropriate way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-26T18:56:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "11N37",
      "60F15"
    ],
    "keywords": [
      "random set",
      "common multiple",
      "poisson limit theorems",
      "appropriate way",
      "brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}