{
  "id": "2404.08387",
  "version": "v1",
  "published": "2024-04-12T10:43:38.000Z",
  "updated": "2024-04-12T10:43:38.000Z",
  "title": "The asymptotic distribution of the scaled remainder for pseudo golden ratio expansions of a continuous random variable",
  "authors": [
    "Ira W. Herbst",
    "Jesper Møller",
    "Anne Marie Svane"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $X=\\sum_{k=1}^\\infty X_k \\beta^{-k}$ be the base-$\\beta$ expansion of a continuous random variable $X$ on the unit interval where $\\beta$ is the positive solution to $\\beta^n = 1 + \\beta + \\cdots + \\beta^{n-1}$ for an integer $n\\ge 2$ (i.e., $\\beta$ is a generalization of the golden mean for which $n=2$). We study the asymptotic distribution and convergence rate of the scaled remainder $\\sum_{k=1}^\\infty X_{m+k} \\beta^{-k}$ when $m$ tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-12T10:43:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F25",
      "62E17",
      "37A50"
    ],
    "keywords": [
      "pseudo golden ratio expansions",
      "continuous random variable",
      "asymptotic distribution",
      "scaled remainder",
      "unit interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}