{
  "id": "2210.03805",
  "version": "v1",
  "published": "2022-10-07T20:28:09.000Z",
  "updated": "2022-10-07T20:28:09.000Z",
  "title": "Non-stationary version of Furstenberg Theorem on random matrix products",
  "authors": [
    "Anton Gorodetski",
    "Victor Kleptsyn"
  ],
  "comment": "33 pages",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "We prove a non-stationary analog of the Furstenberg Theorem on random matrix products (that can be considered as a matrix version of the law of large numbers). Namely, under a suitable genericity conditions the sequence of norms of random products of independent but not necessarily identically distributed $\\SL(d, \\mathbb{R})$ matrices grow exponentially fast, and there exists a non-random sequence that almost surely describes asymptotical behaviour of that sequence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-07T20:28:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37H15",
      "37A50",
      "60F10",
      "60F15",
      "60B20"
    ],
    "keywords": [
      "random matrix products",
      "furstenberg theorem",
      "non-stationary version",
      "matrices grow exponentially fast",
      "non-random sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}