{
  "id": "1801.03308",
  "version": "v1",
  "published": "2018-01-10T11:00:01.000Z",
  "updated": "2018-01-10T11:00:01.000Z",
  "title": "On minimal actions of countable groups",
  "authors": [
    "Eli Glasner",
    "Benjamin Weiss"
  ],
  "comment": "An invited review",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "Our purpose here is to review some recent developments in the theory of dynamical systems whose common theme is a link between minimal dynamical systems, certain Ramsey type combinatorial properties, and the Lovasz local lemma (LLL). For a general countable group G the two classes of minimal systems we will deal with are (I) the minimal subsystems of the {\\em subgroup system} (Sub(G), G), called URS's (uniformly recurrent subgroups), and (II) minimal {\\em subshifts}; i.e. subsystems of the binary Bernoulli G-shift ({0, 1}^G, {\\sig_g}_{g \\in G}).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-10T11:00:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H20",
      "05D10",
      "37A50",
      "20E99",
      "37B10"
    ],
    "keywords": [
      "countable group",
      "minimal actions",
      "ramsey type combinatorial properties",
      "binary bernoulli g-shift",
      "lovasz local lemma"
    ],
    "tags": [
      "review article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}