{
  "id": "2103.04467",
  "version": "v1",
  "published": "2021-03-07T22:06:52.000Z",
  "updated": "2021-03-07T22:06:52.000Z",
  "title": "Metastability and maximal-entropy joinings of Gibbs measures on finitely-generated groups",
  "authors": [
    "Christopher Shriver"
  ],
  "comment": "33 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.DS",
    "math.MP"
  ],
  "abstract": "We prove a metastability result for finitary microstates which are good models for a Gibbs measure for a nearest-neighbor interaction on a finitely-generated group. This is used to show that any maximal-entropy joining of two such Gibbs states is a relative product over the tail $\\sigma$-algebra, except in degenerate cases. We also use results on extremal cuts of random graphs to further investigate optimal self-joinings of the Ising model on a free group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-07T22:06:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gibbs measure",
      "finitely-generated group",
      "maximal-entropy joining",
      "metastability result",
      "random graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}