---
_id: '1010'
abstract:
- lang: eng
text: 'We prove a local law in the bulk of the spectrum for random Gram matrices
XX∗, a generalization of sample covariance matrices, where X is a large matrix
with independent, centered entries with arbitrary variances. The limiting eigenvalue
density that generalizes the Marchenko-Pastur law is determined by solving a system
of nonlinear equations. Our entrywise and averaged local laws are on the optimal
scale with the optimal error bounds. They hold both in the square case (hard edge)
and in the properly rectangular case (soft edge). In the latter case we also establish
a macroscopic gap away from zero in the spectrum of XX∗. '
article_number: '25'
article_processing_charge: No
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Alt J, Erdös L, Krüger TH. Local law for random Gram matrices. Electronic
Journal of Probability. 2017;22. doi:10.1214/17-EJP42
apa: Alt, J., Erdös, L., & Krüger, T. H. (2017). Local law for random Gram matrices.
Electronic Journal of Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/17-EJP42
chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Local Law for Random
Gram Matrices.” Electronic Journal of Probability. Institute of Mathematical
Statistics, 2017. https://doi.org/10.1214/17-EJP42.
ieee: J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,”
Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics,
2017.
ista: Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic
Journal of Probability. 22, 25.
mla: Alt, Johannes, et al. “Local Law for Random Gram Matrices.” Electronic Journal
of Probability, vol. 22, 25, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP42.
short: J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017).
date_created: 2018-12-11T11:49:40Z
date_published: 2017-03-08T00:00:00Z
date_updated: 2023-09-22T09:45:23Z
day: '08'
ddc:
- '510'
- '539'
department:
- _id: LaEr
doi: 10.1214/17-EJP42
ec_funded: 1
external_id:
arxiv:
- '1606.07353'
isi:
- '000396611900025'
file:
- access_level: open_access
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:39Z
date_updated: 2018-12-12T10:13:39Z
file_id: '5024'
file_name: IST-2017-807-v1+1_euclid.ejp.1488942016.pdf
file_size: 639384
relation: main_file
file_date_updated: 2018-12-12T10:13:39Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Electronic Journal of Probability
publication_identifier:
issn:
- '10836489'
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6386'
pubrep_id: '807'
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Local law for random Gram matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 22
year: '2017'
...