{
  "id": "2111.10232",
  "version": "v2",
  "published": "2021-11-18T15:23:04.000Z",
  "updated": "2022-02-09T15:07:28.000Z",
  "title": "Asymptotics of entries of products of nonnegative 2-by-2 matrices",
  "authors": [
    "Hua-Ming Wang"
  ],
  "comment": "14 pages; we add some new results in this edition",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $M$ and $M_n,n\\ge1$ be nonnegative 2-by-2 matrices such that $\\lim_{n\\rightarrow\\infty}M_n=M.$ It is usually hard to estimate the entries of $M_{k+1}\\cdots M_{k+n}$ which are useful in many applications. In this paper, under a mild condition, we show that up to a multiplication of some positive constants, entries of $M_{k+1}\\cdots M_{k+n}$ are asymptotically the same as $\\xi_{k+1}\\cdots \\xi_{k+n},$ the product of the tails of a continued fraction which is related to the matrices $M_k,k\\ge1,$ as $n\\rightarrow\\infty.$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-09T15:07:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B48",
      "11A55"
    ],
    "keywords": [
      "asymptotics",
      "nonnegative",
      "mild condition",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}