---
_id: '1012'
abstract:
- lang: eng
  text: We prove a new central limit theorem (CLT) for the difference of linear eigenvalue
    statistics of a Wigner random matrix H and its minor H and find that the fluctuation
    is much smaller than the fluctuations of the individual linear statistics, as
    a consequence of the strong correlation between the eigenvalues of H and H. In
    particular, our theorem identifies the fluctuation of Kerov's rectangular Young
    diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic
    shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel
    measure follow the same limiting shape. For this, algebraically motivated, ensemble
    a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar
    to our result but the variance is different, indicating that the analogy between
    the two models has its limitations. Moreover, our theorem shows that Borodin's
    result [7] on the convergence of the spectral distribution of Wigner matrices
    to a Gaussian free field also holds in derivative sense.
article_processing_charge: No
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Dominik J
  full_name: Schröder, Dominik J
  id: 408ED176-F248-11E8-B48F-1D18A9856A87
  last_name: Schröder
  orcid: 0000-0002-2904-1856
citation:
  ama: Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing
    wigner eigenvalues. <i>International Mathematics Research Notices</i>. 2018;2018(10):3255-3298.
    doi:<a href="https://doi.org/10.1093/imrn/rnw330">10.1093/imrn/rnw330</a>
  apa: Erdös, L., &#38; Schröder, D. J. (2018). Fluctuations of rectangular young
    diagrams of interlacing wigner eigenvalues. <i>International Mathematics Research
    Notices</i>. Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnw330">https://doi.org/10.1093/imrn/rnw330</a>
  chicago: Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young
    Diagrams of Interlacing Wigner Eigenvalues.” <i>International Mathematics Research
    Notices</i>. Oxford University Press, 2018. <a href="https://doi.org/10.1093/imrn/rnw330">https://doi.org/10.1093/imrn/rnw330</a>.
  ieee: L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of
    interlacing wigner eigenvalues,” <i>International Mathematics Research Notices</i>,
    vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.
  ista: Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of
    interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10),
    3255–3298.
  mla: Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young
    Diagrams of Interlacing Wigner Eigenvalues.” <i>International Mathematics Research
    Notices</i>, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:<a
    href="https://doi.org/10.1093/imrn/rnw330">10.1093/imrn/rnw330</a>.
  short: L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018
    (2018) 3255–3298.
date_created: 2018-12-11T11:49:41Z
date_published: 2018-05-18T00:00:00Z
date_updated: 2023-09-22T09:44:21Z
day: '18'
department:
- _id: LaEr
doi: 10.1093/imrn/rnw330
ec_funded: 1
external_id:
  arxiv:
  - '1608.05163'
  isi:
  - '000441668300009'
intvolume: '      2018'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1608.05163
month: '05'
oa: 1
oa_version: Preprint
page: 3255-3298
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - '10737928'
publication_status: published
publisher: Oxford University Press
publist_id: '6383'
quality_controlled: '1'
related_material:
  record:
  - id: '6179'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 2018
year: '2018'
...