---
_id: '6488'
abstract:
- lang: eng
  text: We prove a central limit theorem for the difference of linear eigenvalue statistics
    of a sample covariance matrix W˜ and its minor W. We find that the fluctuation
    of this difference is much smaller than those of the individual linear statistics,
    as a consequence of the strong correlation between the eigenvalues of W˜ and W.
    Our result identifies the fluctuation of the spatial derivative of the approximate
    Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar
    result for Wigner matrices, for sample covariance matrices, the fluctuation may
    entirely vanish.
article_number: '2050006'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
  full_name: Cipolloni, Giorgio
  id: 42198EFA-F248-11E8-B48F-1D18A9856A87
  last_name: Cipolloni
  orcid: 0000-0002-4901-7992
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: 'Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics
    for sample covariance matrices. <i>Random Matrices: Theory and Application</i>.
    2020;9(3). doi:<a href="https://doi.org/10.1142/S2010326320500069">10.1142/S2010326320500069</a>'
  apa: 'Cipolloni, G., &#38; Erdös, L. (2020). Fluctuations for differences of linear
    eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory
    and Application</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S2010326320500069">https://doi.org/10.1142/S2010326320500069</a>'
  chicago: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of
    Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices:
    Theory and Application</i>. World Scientific Publishing, 2020. <a href="https://doi.org/10.1142/S2010326320500069">https://doi.org/10.1142/S2010326320500069</a>.'
  ieee: 'G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue
    statistics for sample covariance matrices,” <i>Random Matrices: Theory and Application</i>,
    vol. 9, no. 3. World Scientific Publishing, 2020.'
  ista: 'Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue
    statistics for sample covariance matrices. Random Matrices: Theory and Application.
    9(3), 2050006.'
  mla: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear
    Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory
    and Application</i>, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020,
    doi:<a href="https://doi.org/10.1142/S2010326320500069">10.1142/S2010326320500069</a>.'
  short: 'G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).'
date_created: 2019-05-26T21:59:14Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2023-08-28T08:38:48Z
day: '01'
department:
- _id: LaEr
doi: 10.1142/S2010326320500069
ec_funded: 1
external_id:
  arxiv:
  - '1806.08751'
  isi:
  - '000547464400001'
intvolume: '         9'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1806.08751
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '665385'
  name: International IST Doctoral Program
publication: 'Random Matrices: Theory and Application'
publication_identifier:
  eissn:
  - '20103271'
  issn:
  - '20103263'
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fluctuations for differences of linear eigenvalue statistics for sample covariance
  matrices
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 9
year: '2020'
...