{
  "id": "1710.05253",
  "version": "v1",
  "published": "2017-10-15T00:42:06.000Z",
  "updated": "2017-10-15T00:42:06.000Z",
  "title": "GOE statistics for Anderson models on antitrees and thin boxes in $\\mathbb{Z}^3$ with deformed Laplacian",
  "authors": [
    "Christian Sadel"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR",
    "math.SP"
  ],
  "abstract": "Sequences of certain finite graphs, antitrees, are constructed along which the Anderson model shows GOE statistics, i.e. a re-scaled eigenvalue process converges to the ${\\rm Sine}_1$ process. The Anderson model on the graph is a random matrix being the sum of the adjacency matrix and a random diagonal matrix with independent identically distributed entries along the diagonal. The strength of the randomness stays fixed, there is no re-scaling with matrix size. These considered random matrices giving GOE statistics can also be viewed as random Schr\\\"odinger operators $\\mathcal{P}\\Delta+\\mathcal{V}$ on thin finite boxes in $\\mathbb{Z}^3$ where the Laplacian $\\Delta$ is deformed by a projection $\\mathcal{P}$ commuting with $\\Delta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-15T00:42:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "82B44",
      "60H25",
      "15B52"
    ],
    "keywords": [
      "anderson model",
      "thin boxes",
      "deformed laplacian",
      "random matrices giving goe statistics",
      "random matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}