{
  "id": "2006.02191",
  "version": "v1",
  "published": "2020-06-03T12:00:08.000Z",
  "updated": "2020-06-03T12:00:08.000Z",
  "title": "Flexibility of statistical properties for smooth systems satisfying the central limit theorem",
  "authors": [
    "Dmitry Dolgopyat",
    "Changguang Dong",
    "Adam Kanigowski",
    "Peter Nándori"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we exhibit new classes of smooth systems which satisfy the Central Limit Theorem (CLT) and have (at least) one of the following properties: (1) zero entropy; (2) weak but not strong mixing; (3) (polynomially) mixing but not $K$; (4) $K$ but not Bernoulli; (5) non Bernoulli and mixing at arbitrary fast polynomial rate. We also give an example of a system satisfying the CLT where the normalizing sequence is regularly varying with index $1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-03T12:00:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "smooth systems satisfying",
      "statistical properties",
      "arbitrary fast polynomial rate",
      "flexibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}