{
  "id": "1910.02999",
  "version": "v1",
  "published": "2019-10-07T18:36:11.000Z",
  "updated": "2019-10-07T18:36:11.000Z",
  "title": "Universality for 1 d random band matrices",
  "authors": [
    "Mariya Shcherbina",
    "Tatyana Shcherbina"
  ],
  "comment": "47 p",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider 1d random Hermitian $N\\times N$ block band matrices consisting of $W\\times W$ random Gaussian blocks (parametrized by $j,k \\in\\Lambda=[1,n]\\cap \\mathbb{Z}$, $N=nW$) with a fixed entry's variance $J_{jk}=W^{-1}(\\delta_{j,k}+\\beta\\Delta_{j,k})$ in each block. Considering the limit $W, n\\to\\infty$, we prove that the behaviour of the second correlation function of such matrices in the bulk of the spectrum, as $W\\gg \\sqrt{N}$, is determined by the Wigner -- Dyson statistics. The method of the proof is based on the rigorous application of supersymmetric transfer matrix approach developed in [Shcherbina, M., Shcherbina, T.:Universality for 1d random band matrices: sigma-model approximation, J.Stat.Phys. 172, p. 627 -- 664 (2018)]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-07T18:36:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universality",
      "1d random band matrices",
      "supersymmetric transfer matrix approach",
      "random gaussian blocks",
      "1d random hermitian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}