{
  "id": "1402.2234",
  "version": "v3",
  "published": "2014-02-10T18:43:20.000Z",
  "updated": "2014-05-23T15:12:05.000Z",
  "title": "Subshifts with slow complexity and simple groups with the Liouville property",
  "authors": [
    "Nicolás Matte Bon"
  ],
  "comment": "18 pages, no figure. Revised version after referee report. Reorganized introduction, added some examples. To appear in GAFA",
  "categories": [
    "math.GR",
    "math.DS",
    "math.PR"
  ],
  "abstract": "We study random walk on topological full groups of subshifts, and show the existence of infinite, finitely generated, simple groups with the Liouville property. Results by Matui and Juschenko-Monod have shown that the derived subgroups of topological full groups of minimal subshifts provide the first examples of finitely generated, simple amenable groups. We show that if the (not necessarily minimal) subshift has a complexity function that grows slowly enough (e.g. linearly), then every symmetric and finitely supported probability measure on the topological full group has trivial Poisson-Furstenberg boundary. We also get explicit upper bounds for the growth of F{\\o}lner sets.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-23T15:12:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple groups",
      "liouville property",
      "slow complexity",
      "topological full group",
      "trivial poisson-furstenberg boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.2234M"
    }
  }
}