{
  "id": "1712.03698",
  "version": "v1",
  "published": "2017-12-11T09:53:37.000Z",
  "updated": "2017-12-11T09:53:37.000Z",
  "title": "Limit laws for random matrix products",
  "authors": [
    "Jordan Emme",
    "Pascal Hubert"
  ],
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "In this short note, we study the behaviour of a product of matrices with a simultaneous renormalization. Namely, for any sequence $(A\\_n)\\_{n\\in \\mathbb{N}}$ of $d\\times d$ complex matrices whose mean $A$ exists and whose norms' means are bounded, the product $\\left(I\\_d + \\frac1n A\\_0 \\right) \\dots \\left(I\\_d + \\frac1n A\\_{n-1} \\right) $ converges towards $\\exp{A}$. We give a dynamical version of this result as well as an illustration with an example of \"random walk\" on horocycles of the hyperbolic disc.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-11T09:53:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrix products",
      "limit laws",
      "hyperbolic disc",
      "complex matrices",
      "random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}