{
  "id": "2010.06146",
  "version": "v1",
  "published": "2020-10-13T03:39:02.000Z",
  "updated": "2020-10-13T03:39:02.000Z",
  "title": "Strongly mixing systems are almost strongly mixing of all orders",
  "authors": [
    "Vitaly Bergelson",
    "Rigoberto Zelada"
  ],
  "comment": "36 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that any strongly mixing action of a countable abelian group on a probability space has higher order mixing properties. This is achieved via introducing and utilizing $\\mathcal R$-limits, a notion of convergence which is based on the classical Ramsey Theorem. $\\mathcal R$-limits are intrinsically connected with a new combinatorial notion of largeness which is similar to but has stronger properties than the classical notions of IP$^*$ and uniform density one. We also demonstrate the versatility of this new approach by obtaining applications to higher order mixing properties of weakly and mildly mixing systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-13T03:39:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A25"
    ],
    "keywords": [
      "strongly mixing systems",
      "higher order mixing properties",
      "uniform density",
      "probability space",
      "stronger properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}