{
  "id": "2108.11634",
  "version": "v1",
  "published": "2021-08-26T08:02:12.000Z",
  "updated": "2021-08-26T08:02:12.000Z",
  "title": "Higher order fluctuations of extremal eigenvalues of sparse random matrices",
  "authors": [
    "Jaehun Lee"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study higher-order fluctuations of extremal eigenvalues of sparse random matrices on the regime $N^{\\epsilon}\\ll q \\ll N^{1/2}$ where $q$ is the sparsity parameter. In the case $N^{1/9}\\ll q\\ll N^{1/6}$, it was known that eigenvalue rigidity can be recovered by removing asymptotically Gaussian fluctuations. We consider the regime $N^{\\epsilon} \\ll q\\ll N^{1/6}$ and apply a higher-order random correction to the spectral edge in order to capture sub-leading order fluctuations of extremal eigenvalues. We establish local semicircle law near the edge under corrections and recover the eigenvalue rigidity by removing asymptotically Gaussian fluctuations arising from higher-order random corrections.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-26T08:02:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20"
    ],
    "keywords": [
      "sparse random matrices",
      "extremal eigenvalues",
      "higher order fluctuations",
      "higher-order random correction",
      "removing asymptotically gaussian fluctuations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}