{
  "id": "2011.09180",
  "version": "v1",
  "published": "2020-11-18T10:03:58.000Z",
  "updated": "2020-11-18T10:03:58.000Z",
  "title": "Integrated density of states of the Anderson Hamiltonian with two-dimensional white noise",
  "authors": [
    "Toyomu Matsuda"
  ],
  "comment": "34 pages, 1 figure",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We construct the integrated density of states of the Anderson Hamiltonian with two-dimensional white noise by proving the convergence of the Dirichlet eigenvalue counting measures associated with the Anderson Hamiltonians on the boxes. We also determine the logarithmic asymptotics of the left tail of the integrated density of states. Furthermore, we apply our result to a moment explosion of the parabolic Anderson model in the plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-18T10:03:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H25",
      "60H20",
      "35J10",
      "35P20",
      "82B44"
    ],
    "keywords": [
      "two-dimensional white noise",
      "anderson hamiltonian",
      "integrated density",
      "dirichlet eigenvalue counting measures",
      "parabolic anderson model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}