{
  "id": "1402.3705",
  "version": "v3",
  "published": "2014-02-15T17:01:10.000Z",
  "updated": "2015-05-30T20:42:51.000Z",
  "title": "Characteristic random subgroups of geometric groups and free abelian groups of infinite rank",
  "authors": [
    "Lewis Bowen",
    "Rostislav Grigorchuk",
    "Rostyslav Kravchenko"
  ],
  "comment": "Comments welcome! This new version classifies automorphism-invariant random subspaces of a locally compact vector space over a finite field and computes finite marginals",
  "categories": [
    "math.GR",
    "math.DS"
  ],
  "abstract": "We show that if $G$ is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then $G$ has $2^{\\aleph_0}$ many continuous ergodic invariant random subgroups. If $G$ is a nonabelian free group then $G$ has $2^{\\aleph_0}$ many continuous $G$-ergodic characteristic random subgroups. We also provide a complete classification of characteristic random subgroups of free abelian groups of countably infinite rank and elementary $p$-groups of countably infinite rank.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-15T14:39:00.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-05-30T20:42:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free abelian groups",
      "geometric groups",
      "ergodic invariant random subgroups",
      "nonabelian free group",
      "countably infinite rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.3705B"
    }
  }
}