---
_id: '15013'
abstract:
- lang: eng
  text: We consider random n×n matrices X with independent and centered entries and
    a general variance profile. We show that the spectral radius of X converges with
    very high probability to the square root of the spectral radius of the variance
    matrix of X when n tends to infinity. We also establish the optimal rate of convergence,
    that is a new result even for general i.i.d. matrices beyond the explicitly solvable
    Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular
    law [arXiv:1612.07776] at the spectral edge.
acknowledgement: Partially supported by ERC Starting Grant RandMat No. 715539 and
  the SwissMap grant of Swiss National Science Foundation. Partially supported by
  ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center
  for Mathematics in Bonn.
article_processing_charge: No
article_type: original
arxiv: 1
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. Spectral radius of random matrices with independent
    entries. <i>Probability and Mathematical Physics</i>. 2021;2(2):221-280. doi:<a
    href="https://doi.org/10.2140/pmp.2021.2.221">10.2140/pmp.2021.2.221</a>
  apa: Alt, J., Erdös, L., &#38; Krüger, T. H. (2021). Spectral radius of random matrices
    with independent entries. <i>Probability and Mathematical Physics</i>. Mathematical
    Sciences Publishers. <a href="https://doi.org/10.2140/pmp.2021.2.221">https://doi.org/10.2140/pmp.2021.2.221</a>
  chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random
    Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>.
    Mathematical Sciences Publishers, 2021. <a href="https://doi.org/10.2140/pmp.2021.2.221">https://doi.org/10.2140/pmp.2021.2.221</a>.
  ieee: J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with
    independent entries,” <i>Probability and Mathematical Physics</i>, vol. 2, no.
    2. Mathematical Sciences Publishers, pp. 221–280, 2021.
  ista: Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent
    entries. Probability and Mathematical Physics. 2(2), 221–280.
  mla: Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent
    Entries.” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2, Mathematical
    Sciences Publishers, 2021, pp. 221–80, doi:<a href="https://doi.org/10.2140/pmp.2021.2.221">10.2140/pmp.2021.2.221</a>.
  short: J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021)
    221–280.
date_created: 2024-02-18T23:01:03Z
date_published: 2021-05-21T00:00:00Z
date_updated: 2024-02-19T08:30:00Z
day: '21'
department:
- _id: LaEr
doi: 10.2140/pmp.2021.2.221
ec_funded: 1
external_id:
  arxiv:
  - '1907.13631'
intvolume: '         2'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1907.13631
month: '05'
oa: 1
oa_version: Preprint
page: 221-280
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Probability and Mathematical Physics
publication_identifier:
  eissn:
  - 2690-1005
  issn:
  - 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral radius of random matrices with independent entries
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2021'
...