{
  "id": "2303.04237",
  "version": "v2",
  "published": "2023-03-07T21:02:29.000Z",
  "updated": "2023-05-29T14:13:49.000Z",
  "title": "Stationary random subgroups in negative curvature",
  "authors": [
    "Ilya Gekhtman",
    "Arie Levit"
  ],
  "comment": "changes in v2: 1. shorter by 5 pages by simplifying an argument 2. includes treatment of positive characteristic case 3. includes a new corollary regarding weak equivalence",
  "categories": [
    "math.GR",
    "math.DS",
    "math.GT",
    "math.PR"
  ],
  "abstract": "We show that discrete stationary random subgroups of isometry groups of Gromov hyperbolic spaces have full limit sets as well as critical exponents bounded from below. This information is used to answer a question of Gelander and show that a rank one locally symmetric space for which the bottom of the spectrum of the Laplace-Beltrami operator is the same as that of its universal cover has unbounded injectivity radius.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-05-29T14:13:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "20F67",
      "20F67",
      "20F67",
      "60G10",
      "43A07",
      "53C35",
      "37H99"
    ],
    "keywords": [
      "negative curvature",
      "discrete stationary random subgroups",
      "gromov hyperbolic spaces",
      "full limit sets",
      "unbounded injectivity radius"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}