{
  "id": "2309.05488",
  "version": "v1",
  "published": "2023-09-11T14:29:51.000Z",
  "updated": "2023-09-11T14:29:51.000Z",
  "title": "Eigenstate thermalisation at the edge for Wigner matrices",
  "authors": [
    "Giorgio Cipolloni",
    "László Erdős",
    "Joscha Henheik"
  ],
  "comment": "45 pages, 1 figure",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices uniformly in the entire spectrum, in particular near the spectral edges, with a bound on the fluctuation that is optimal for any observable. This complements earlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math., Sigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv: 2303.11142) that were restricted either to the bulk of the spectrum or to special observables. As a main ingredient, we prove a new multi-resolvent local law that optimally accounts for the edge scaling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-11T14:29:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "82B10",
      "58J51"
    ],
    "keywords": [
      "wigner matrices",
      "multi-resolvent local law",
      "complements earlier works",
      "eigenstate thermalisation hypothesis",
      "entire spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}