{
  "id": "1307.7490",
  "version": "v3",
  "published": "2013-07-29T07:58:15.000Z",
  "updated": "2016-02-09T14:13:17.000Z",
  "title": "Symmetric Birkhoff sums in infinite ergodic theory",
  "authors": [
    "Jon. Aaronson",
    "Zemer Kosloff",
    "Benjamin Weiss"
  ],
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "We show that the absolutely normalized, symmetric Birkhoff sums of positive integrable functions in infinite, ergodic systems never converge pointwise even though they may be almost surely bounded away from zero and infinity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-14T06:32:07.000Z",
      "comment": "Added theorem 4",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-02-09T14:13:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric birkhoff sums",
      "infinite ergodic theory",
      "ergodic systems",
      "positive integrable functions",
      "surely bounded away"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7490A"
    }
  }
}