---
_id: '17375'
abstract:
- lang: eng
  text: We consider the spectral radius of a large random matrix X with independent,
    identically distributed entries. We show that its typical size is given by a precise
    three-term asymptotics with an optimal error term beyond the radius of the celebrated
    circular law. The coefficients in this asymptotics are universal but they differ
    from a similar asymptotics recently proved for the rightmost eigenvalue of X in
    Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated
    spectral radius, we need to establish a new decorrelation mechanism for the low-lying
    singular values of X − z for different complex shift parameters z using the Dyson
    Brownian Motion.
acknowledgement: L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond”
  Grant No. 101020331.
article_number: '063302'
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
- first_name: Yuanyuan
  full_name: Xu, Yuanyuan
  id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3
  last_name: Xu
  orcid: 0000-0003-1559-1205
citation:
  ama: Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of
    a large random matrix. <i>Journal of Mathematical Physics</i>. 2024;65(6). doi:<a
    href="https://doi.org/10.1063/5.0209705">10.1063/5.0209705</a>
  apa: Cipolloni, G., Erdös, L., &#38; Xu, Y. (2024). Precise asymptotics for the
    spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>.
    AIP Publishing. <a href="https://doi.org/10.1063/5.0209705">https://doi.org/10.1063/5.0209705</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics
    for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical
    Physics</i>. AIP Publishing, 2024. <a href="https://doi.org/10.1063/5.0209705">https://doi.org/10.1063/5.0209705</a>.
  ieee: G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius
    of a large random matrix,” <i>Journal of Mathematical Physics</i>, vol. 65, no.
    6. AIP Publishing, 2024.
  ista: Cipolloni G, Erdös L, Xu Y. 2024. Precise asymptotics for the spectral radius
    of a large random matrix. Journal of Mathematical Physics. 65(6), 063302.
  mla: Cipolloni, Giorgio, et al. “Precise Asymptotics for the Spectral Radius of
    a Large Random Matrix.” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6,
    063302, AIP Publishing, 2024, doi:<a href="https://doi.org/10.1063/5.0209705">10.1063/5.0209705</a>.
  short: G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024).
corr_author: '1'
date_created: 2024-08-04T22:01:22Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2025-09-08T08:44:57Z
day: '01'
department:
- _id: LaEr
doi: 10.1063/5.0209705
ec_funded: 1
external_id:
  arxiv:
  - '2210.15643'
  isi:
  - '001252240700002'
intvolume: '        65'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2210.15643
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Mathematical Physics
publication_identifier:
  issn:
  - 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Precise asymptotics for the spectral radius of a large random matrix
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 65
year: '2024'
...