---
_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
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. Random Matrices: Theory and Application.
2020;9(3). doi:10.1142/S2010326320500069'
apa: 'Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear
eigenvalue statistics for sample covariance matrices. Random Matrices: Theory
and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069'
chicago: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of
Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices:
Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.'
ieee: 'G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue
statistics for sample covariance matrices,” Random Matrices: Theory and Application,
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.” Random Matrices: Theory
and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020,
doi:10.1142/S2010326320500069.'
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'
...