{
  "id": "2203.13545",
  "version": "v1",
  "published": "2022-03-25T09:59:09.000Z",
  "updated": "2022-03-25T09:59:09.000Z",
  "title": "Automorphism groups of random substitution subshifts",
  "authors": [
    "Robbert Fokkink",
    "Dan Rust",
    "Ville Salo"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are countable, non-amenable and non-residually finite. To show this, we introduce the concept of shuffles and generalised shuffles for random substitutions, as well as a local version of recognisability for random substitutions that will be of independent interest. Without recognisability, we need a more refined notion of recognisable words in order to understand their automorphisms. We show that the existence of a single recognisable word is often enough to embed the automorphism group of a full shift in the automorphism group of the random substitution subshift.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-25T09:59:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37A50",
      "37B40",
      "52C23"
    ],
    "keywords": [
      "automorphism group",
      "random substitution subshift",
      "full shift",
      "infinite simple subgroup",
      "local version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}