{
  "id": "2203.01059",
  "version": "v1",
  "published": "2022-03-02T12:18:39.000Z",
  "updated": "2022-03-02T12:18:39.000Z",
  "title": "Principal Eigenvalue and Landscape Function of the Anderson Model on a Large Box",
  "authors": [
    "Daniel Sánchez-Mendoza"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We state a precise formulation of a conjecture concerning the product of the principal eigenvalue and the sup-norm of the landscape function of the Anderson model restricted to a large box. We first provide the asymptotic of the principal eigenvalue as the size of the box grows and then use it to give a partial proof of the conjecture. For a special case in one dimension we give a complete proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-02T12:18:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal eigenvalue",
      "anderson model",
      "landscape function",
      "large box",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}