{
  "id": "2007.05862",
  "version": "v1",
  "published": "2020-07-11T22:06:52.000Z",
  "updated": "2020-07-11T22:06:52.000Z",
  "title": "A Dobrushin-Lanford-Ruelle theorem for irreducible sofic shifts",
  "authors": [
    "Luísa Borsato",
    "Sophie MacDonald"
  ],
  "comment": "14 pages, 1 diagram",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that for a potential with summable variations on an irreducible sofic shift in one dimension, the equilibrium measures are precisely the shift-invariant Gibbs measures. The main tool in the proof is a preservation of Gibbsianness result for almost invertible factor codes on irreducible shifts of finite type, which we then extend to finite-to-one codes by applying the results about equilibrium measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-11T22:06:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "37B10"
    ],
    "keywords": [
      "irreducible sofic shift",
      "dobrushin-lanford-ruelle theorem",
      "equilibrium measures",
      "shift-invariant gibbs measures",
      "invertible factor codes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}