{
  "id": "1903.12222",
  "version": "v1",
  "published": "2019-03-28T18:56:10.000Z",
  "updated": "2019-03-28T18:56:10.000Z",
  "title": "On the continuity of the integrated density of states in the disorder",
  "authors": [
    "Mira Shamis"
  ],
  "comment": "9 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR",
    "math.SP"
  ],
  "abstract": "Recently, Hislop and Marx studied the dependence of the integrated density of states on the underlying probability distribution for a class of discrete random Schr\\\"odinger operators, and established a quantitative form of continuity in weak* topology. We develop an alternative approach to the problem, based on Ky Fan inequalities, and establish a sharp version of the estimate of Hislop and Marx. We also consider a corresponding problem for continual random Schr\\\"odinger operators on $\\R^d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-28T18:56:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrated density",
      "continuity",
      "ky fan inequalities",
      "sharp version",
      "probability distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}