{
  "id": "2106.00514",
  "version": "v1",
  "published": "2021-06-01T14:17:13.000Z",
  "updated": "2021-06-01T14:17:13.000Z",
  "title": "Entropy and the Discrete Central Limit Theorem",
  "authors": [
    "Lampros Gavalakis",
    "Ioannis Kontoyiannis"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of $n$ independent and identically distributed lattice random variables and an appropriately discretised Gaussian, vanishes as $n\\to\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-01T14:17:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "94A17",
      "60E15"
    ],
    "keywords": [
      "discrete central limit theorem",
      "discrete random variables",
      "identically distributed lattice random variables",
      "elementary arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}