{
  "id": "2012.03017",
  "version": "v1",
  "published": "2020-12-05T12:16:44.000Z",
  "updated": "2020-12-05T12:16:44.000Z",
  "title": "Lower bounds on Anderson-localised eigenfunctions on a strip",
  "authors": [
    "Ilya Goldsheid",
    "Sasha Sodin"
  ],
  "comment": "19 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR",
    "math.SP"
  ],
  "abstract": "It is known that the eigenfunctions of a random Schr\\\"odinger operator on a strip decay exponentially, and that the rate of decay is not slower than prescribed by the slowest Lyapunov exponent. A variery of heuristic arguments suggest that no eigenfunction can decay faster than at this rate. We make a step towards this conjecture by showing that, for each eigenfunction, the rate of exponential decay along any subsequence is strictly slower than the fastest Lyapunov exponent, and that there exists a subsequence along which it is equal to the slowest Lyapunov exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-05T12:16:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bounds",
      "anderson-localised eigenfunctions",
      "slowest lyapunov exponent",
      "fastest lyapunov exponent",
      "heuristic arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}