{
  "id": "2210.11381",
  "version": "v1",
  "published": "2022-10-20T16:21:08.000Z",
  "updated": "2022-10-20T16:21:08.000Z",
  "title": "Asymptotic behaviors of the integrated density of states for random Schrödinger operators associated with Gibbs Point Processes",
  "authors": [
    "Yuta Nakagawa"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The asymptotic behaviors of the integrated density of states $N(\\lambda)$ of Schr\\\"odinger operators with nonpositive potentials associated with Gibbs point processes are studied. It is shown that for some Gibbs point processes, the leading terms of $N(\\lambda)$ as $\\lambda\\downarrow-\\infty$ coincide with that for a Poisson point process, which is known. Moreover, for some Gibbs point processes corresponding to pairwise interactions, the leading terms of $N(\\lambda)$ as $\\lambda\\downarrow-\\infty$ are determined, which are different from that for a Poisson point process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-20T16:21:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "60G55",
      "60G60",
      "60K35"
    ],
    "keywords": [
      "random schrödinger operators",
      "asymptotic behaviors",
      "integrated density",
      "poisson point process",
      "leading terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}