{
  "id": "2305.09835",
  "version": "v1",
  "published": "2023-05-16T22:34:55.000Z",
  "updated": "2023-05-16T22:34:55.000Z",
  "title": "Invariant measures of Toeplitz subshifts on non-amenable groups",
  "authors": [
    "Paulina Cecchi Bernales",
    "María Isabel Cortez",
    "Jaime Gómez"
  ],
  "comment": "26 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $G$ be a countable residually finite group (for instance $\\mathbb{F}_2$) and let $\\overleftarrow{G}$ be a totally disconnected metric compactification of $G$ equipped with the action of $G$ by left multiplication. For every $r\\geq 1$ we construct a Toeplitz $G$-subshift $(X,\\sigma,G)$, which is an almost one-to-one extension of $\\overleftarrow{G}$, having $r$ ergodic measures $\\nu_1, \\cdots,\\nu_r$ such that for every $1\\leq i\\leq r$ the measure-theoretic dynamical systems $(X,\\sigma,G,\\nu_i)$ is isomorphic to $\\overleftarrow{G}$ endowed with the Haar measure. The construction we propose is general (for amenable and non-amenable residually finite groups), however, we point out the differences and obstructions that could appear when the acting group is not amenable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-16T22:34:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37B10"
    ],
    "keywords": [
      "invariant measures",
      "toeplitz subshifts",
      "non-amenable groups",
      "left multiplication",
      "non-amenable residually finite groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}