{
  "id": "2408.07398",
  "version": "v1",
  "published": "2024-08-14T09:18:10.000Z",
  "updated": "2024-08-14T09:18:10.000Z",
  "title": "Proximality, stability, and central limit theorem for random maps on an interval",
  "authors": [
    "Sander C. Hille",
    "Katarzyna Horbacz",
    "Hanna Oppelmayer",
    "Tomasz Szarek"
  ],
  "categories": [
    "math.DS",
    "math.FA",
    "math.PR"
  ],
  "abstract": "Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\\mu$-injectivity and some mild assumptions, then proximality, asymptotic stability and a central limit theorem hold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-14T09:18:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A50",
      "37A25",
      "60F05",
      "60G52",
      "60G53",
      "60G10"
    ],
    "keywords": [
      "random maps",
      "proximality",
      "central limit theorem hold",
      "stochastic dynamical systems",
      "mild assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}