---
_id: '14667'
abstract:
- lang: eng
  text: 'For large dimensional non-Hermitian random matrices X with real or complex
    independent, identically distributed, centered entries, we consider the fluctuations
    of f (X) as a matrix where f is an analytic function around the spectrum of X.
    We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits
    Gaussian fluctuations as the matrix size grows to infinity, which consists of
    two independent modes corresponding to the tracial and traceless parts of A. We
    find a new formula for the variance of the traceless part that involves the Frobenius
    norm of A and the L2-norm of f on the boundary of the limiting spectrum. '
- lang: fre
  text: On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne
    de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction
    analytique sur un domaine qui contient le spectre de X. On prouve que, pour une
    matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A
    sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant
    aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie
    pour la variance de la composante de trace nulle, qui fait intervenir la norme
    de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.
acknowledgement: "The first author was partially supported by ERC Advanced Grant “RMTBeyond”
  No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond”
  No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated
  editor for carefully reading this paper and providing helpful comments that improved
  the quality of the article. Also the authors would like to thank Peter Forrester
  for pointing out the reference [12] that was absent in the previous version of the
  manuscript."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Hong Chang
  full_name: Ji, Hong Chang
  id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
  last_name: Ji
citation:
  ama: Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. <i>Annales
    de l’institut Henri Poincare (B) Probability and Statistics</i>. 2023;59(4):2083-2105.
    doi:<a href="https://doi.org/10.1214/22-AIHP1304">10.1214/22-AIHP1304</a>
  apa: Erdös, L., &#38; Ji, H. C. (2023). Functional CLT for non-Hermitian random
    matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>.
    Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/22-AIHP1304">https://doi.org/10.1214/22-AIHP1304</a>
  chicago: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
    Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>.
    Institute of Mathematical Statistics, 2023. <a href="https://doi.org/10.1214/22-AIHP1304">https://doi.org/10.1214/22-AIHP1304</a>.
  ieee: L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,”
    <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol.
    59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.
  ista: Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales
    de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.
  mla: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
    Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>,
    vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:<a
    href="https://doi.org/10.1214/22-AIHP1304">10.1214/22-AIHP1304</a>.
  short: L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and
    Statistics 59 (2023) 2083–2105.
corr_author: '1'
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2025-09-09T13:41:08Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-AIHP1304
ec_funded: 1
external_id:
  arxiv:
  - '2112.11382'
  isi:
  - '001098456400010'
intvolume: '        59'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2112.11382
month: '11'
oa: 1
oa_version: Preprint
page: 2083-2105
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
  issn:
  - 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functional CLT for non-Hermitian random matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 59
year: '2023'
...