{
  "id": "2005.04911",
  "version": "v1",
  "published": "2020-05-11T08:08:37.000Z",
  "updated": "2020-05-11T08:08:37.000Z",
  "title": "Limit theorems for random points in a simplex",
  "authors": [
    "Anastas Baci",
    "Zakhar Kabluchko",
    "Joscha Prochno",
    "Mathias Sonnleitner",
    "Christoph Thaele"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work the $\\ell_q$-norms of points chosen uniformly at random in a centered regular simplex in high dimensions are studied. Berry-Esseen bounds in the regime $1\\leq q < \\infty$ are derived and complemented by a non-central limit theorem together with moderate and large deviations in the case where $q=\\infty$. A comparison with corresponding results for $\\ell_p^n$-balls is carried out as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-11T08:08:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60F10",
      "52A23",
      "60D05"
    ],
    "keywords": [
      "random points",
      "non-central limit theorem",
      "large deviations",
      "berry-esseen bounds",
      "centered regular simplex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}