---
res:
  bibo_abstract:
  - "We consider the fluctuations of regular functions f of a Wigner matrix W viewed
    as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W),
    which is equivalent to the customary linear statistics of eigenvalues, we show
    that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic
    matrix A. We identify three different and asymptotically independent modes of
    this fluctuation, corresponding to the tracial part, the traceless diagonal part
    and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find
    that the off-diagonal modes fluctuate on a much smaller scale than the tracial
    mode. As a main motivation to study CLT in such generality on small mesoscopic
    scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis
    (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps
    with any deterministic matrix are asymptotically Gaussian after a small spectral
    averaging. Finally, in the macroscopic regime our result also generalizes (Zh.
    Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover
    ensembles in between. The main technical inputs are the recent\r\nmultiresolvent
    local laws with traceless deterministic matrices from the companion paper (Comm.
    Math. Phys. 388 (2021) 1005–1048).@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Giorgio
      foaf_name: Cipolloni, Giorgio
      foaf_surname: Cipolloni
      foaf_workInfoHomepage: http://www.librecat.org/personId=42198EFA-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-4901-7992
  - foaf_Person:
      foaf_givenName: László
      foaf_name: Erdös, László
      foaf_surname: Erdös
      foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0001-5366-9603
  - foaf_Person:
      foaf_givenName: Dominik J
      foaf_name: Schröder, Dominik J
      foaf_surname: Schröder
      foaf_workInfoHomepage: http://www.librecat.org/personId=408ED176-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-2904-1856
  bibo_doi: 10.1214/22-AAP1820
  bibo_issue: '1'
  bibo_volume: 33
  dct_date: 2023^xs_gYear
  dct_identifier:
  - UT:000946432400015
  dct_isPartOf:
  - http://id.crossref.org/issn/1050-5164
  dct_language: eng
  dct_publisher: Institute of Mathematical Statistics@
  dct_title: Functional central limit theorems for Wigner matrices@
...