{
  "id": "2206.05545",
  "version": "v1",
  "published": "2022-06-11T15:21:04.000Z",
  "updated": "2022-06-11T15:21:04.000Z",
  "title": "Dynamical Localization for Random Band Matrices up to $W\\ll N^{1/4}$",
  "authors": [
    "Giorgio Cipolloni",
    "Ron Peled",
    "Jeffrey Schenker",
    "Jacob Shapiro"
  ],
  "comment": "23 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider a large class of $N\\times N$ Gaussian random band matrices with band-width $W$, and prove that for $W \\ll N^{1/4}$ they exhibit Anderson localization at all energies. To prove this result, we rely on the fractional moment method, and on the so-called Mermin-Wagner shift (a common tool in statistical mechanics).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-11T15:21:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamical localization",
      "gaussian random band matrices",
      "fractional moment method",
      "large class",
      "anderson localization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}