{
  "id": "2303.11142",
  "version": "v1",
  "published": "2023-03-20T14:21:24.000Z",
  "updated": "2023-03-20T14:21:24.000Z",
  "title": "Fluctuations in Quantum Unique Ergodicity at the Spectral Edge",
  "authors": [
    "Lucas Benigni",
    "Nixia Chen",
    "Patrick Lopatto",
    "Xiaoyu Xie"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the eigenvector mass distribution of an $N\\times N$ Wigner matrix on a set of coordinates $I$ satisfying $| I | \\ge c N$ for some constant $c >0$. For eigenvectors corresponding to eigenvalues at the spectral edge, we show that the sum of the mass on these coordinates converges to a Gaussian in the $N \\rightarrow \\infty$ limit, after a suitable rescaling and centering. The proof proceeds by a two moment matching argument. We directly compare edge eigenvector observables of an arbitrary Wigner matrix to those of a Gaussian matrix, which may be computed explicitly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-20T14:21:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum unique ergodicity",
      "spectral edge",
      "fluctuations",
      "eigenvector mass distribution",
      "arbitrary wigner matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}