{
  "id": "1804.06166",
  "version": "v1",
  "published": "2018-04-17T11:15:36.000Z",
  "updated": "2018-04-17T11:15:36.000Z",
  "title": "Regular expansion for the characteristic exponent of a product of $2 \\times 2$ random matrices",
  "authors": [
    "Benjamin Havret"
  ],
  "comment": "24 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider a product of $2 \\times 2$ random matrices which appears in the physics literature in the analysis of some 1D disordered models. These matrices depend on a parameter $\\epsilon >0$ and on a positive random variable $Z$. Derrida and Hilhorst (J Phys A 16:2641, 1983, \\S 3) predict that the corresponding characteristic exponent has a regular expansion with respect to $\\epsilon$ up to --- and not further --- an order determined by the distribution of $Z$. We give a rigorous proof of that statement. We also study the singular term which breaks that expansion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-17T11:15:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "60B20",
      "37H15"
    ],
    "keywords": [
      "random matrices",
      "regular expansion",
      "1d disordered models",
      "physics literature",
      "corresponding characteristic exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}