{
  "id": "2305.06009",
  "version": "v1",
  "published": "2023-05-10T09:34:40.000Z",
  "updated": "2023-05-10T09:34:40.000Z",
  "title": "Continuity of the Lyapunov exponents of random matrix products",
  "authors": [
    "Artur Avila",
    "Alex Eskin",
    "Marcelo Viana"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that the Lyapunov exponents of random products in a (real or complex) matrix group depends continuously on the matrix coefficients and probability weights. More generally, the Lyapunov exponents of the random product defined by any compactly supported probability distribution on $GL(d)$ vary continuously with the distribution, in a natural topology corresponding to weak$^*$-closeness of the distributions and Hausdorff-closeness of their supports.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-10T09:34:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37H15",
      "37D25"
    ],
    "keywords": [
      "random matrix products",
      "lyapunov exponents",
      "random product",
      "continuity",
      "matrix group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}