---
_id: '550'
abstract:
- lang: eng
  text: For large random matrices X with independent, centered entries but not necessarily
    identical variances, the eigenvalue density of XX* is well-approximated by a deterministic
    measure on ℝ. We show that the density of this measure has only square and cubic-root
    singularities away from zero. We also extend the bulk local law in [5] to the
    vicinity of these singularities.
article_number: '63'
author:
- first_name: Johannes
  full_name: Alt, Johannes
  id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
  last_name: Alt
citation:
  ama: Alt J. Singularities of the density of states of random Gram matrices. <i>Electronic
    Communications in Probability</i>. 2017;22. doi:<a href="https://doi.org/10.1214/17-ECP97">10.1214/17-ECP97</a>
  apa: Alt, J. (2017). Singularities of the density of states of random Gram matrices.
    <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics.
    <a href="https://doi.org/10.1214/17-ECP97">https://doi.org/10.1214/17-ECP97</a>
  chicago: Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.”
    <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics,
    2017. <a href="https://doi.org/10.1214/17-ECP97">https://doi.org/10.1214/17-ECP97</a>.
  ieee: J. Alt, “Singularities of the density of states of random Gram matrices,”
    <i>Electronic Communications in Probability</i>, vol. 22. Institute of Mathematical
    Statistics, 2017.
  ista: Alt J. 2017. Singularities of the density of states of random Gram matrices.
    Electronic Communications in Probability. 22, 63.
  mla: Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.”
    <i>Electronic Communications in Probability</i>, vol. 22, 63, Institute of Mathematical
    Statistics, 2017, doi:<a href="https://doi.org/10.1214/17-ECP97">10.1214/17-ECP97</a>.
  short: J. Alt, Electronic Communications in Probability 22 (2017).
date_created: 2018-12-11T11:47:07Z
date_published: 2017-11-21T00:00:00Z
date_updated: 2023-09-07T12:38:08Z
day: '21'
ddc:
- '539'
department:
- _id: LaEr
doi: 10.1214/17-ECP97
ec_funded: 1
file:
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  creator: system
  date_created: 2018-12-12T10:08:04Z
  date_updated: 2020-07-14T12:47:00Z
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file_date_updated: 2020-07-14T12:47:00Z
has_accepted_license: '1'
intvolume: '        22'
language:
- iso: eng
month: '11'
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 Communications in Probability
publication_identifier:
  issn:
  - 1083589X
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '7265'
pubrep_id: '926'
quality_controlled: '1'
related_material:
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    relation: dissertation_contains
    status: public
scopus_import: 1
status: public
title: Singularities of the density of states of random Gram matrices
tmp:
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  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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 22
year: '2017'
...