---
OA_place: repository
OA_type: green
_id: '23112'
abstract:
- lang: eng
  text: We study the joint spectral properties of two coupled random matrices H(1)
    and H(2), which are either real symmetric or complex Hermitian. The entries of
    these matrices exhibit polynomially decaying correlations, both within each matrix
    and between them. Surprisingly, we find that under extremely weak decorrelation
    condition, permitting H(1) and H(2) to be almost fully correlated, the fluctuations
    of their individual eigenvalues in the bulk of the spectrum are still asymptotically
    independent. Furthermore, we demonstrate that this decorrelation condition is
    optimal.
acknowledgement: The author is grateful to László Erdős and Giorgio Cipolloni for
  suggesting the project and fruitful discussions. The author was supported by the
  ERC Advanced Grant “RMTBeyond” No. 101020331.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Oleksii
  full_name: Kolupaiev, Oleksii
  id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
  last_name: Kolupaiev
  orcid: 0000-0003-1491-4623
citation:
  ama: Kolupaiev O. Spectral independence of almost fully correlated random matrices.
    <i>Bernoulli</i>. 2026;32(4):2999-3023. doi:<a href="https://doi.org/10.3150/26-bej1976">10.3150/26-bej1976</a>
  apa: Kolupaiev, O. (2026). Spectral independence of almost fully correlated random
    matrices. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and
    Probability. <a href="https://doi.org/10.3150/26-bej1976">https://doi.org/10.3150/26-bej1976</a>
  chicago: Kolupaiev, Oleksii. “Spectral Independence of Almost Fully Correlated Random
    Matrices.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and
    Probability, 2026. <a href="https://doi.org/10.3150/26-bej1976">https://doi.org/10.3150/26-bej1976</a>.
  ieee: O. Kolupaiev, “Spectral independence of almost fully correlated random matrices,”
    <i>Bernoulli</i>, vol. 32, no. 4. Bernoulli Society for Mathematical Statistics
    and Probability, pp. 2999–3023, 2026.
  ista: Kolupaiev O. 2026. Spectral independence of almost fully correlated random
    matrices. Bernoulli. 32(4), 2999–3023.
  mla: Kolupaiev, Oleksii. “Spectral Independence of Almost Fully Correlated Random
    Matrices.” <i>Bernoulli</i>, vol. 32, no. 4, Bernoulli Society for Mathematical
    Statistics and Probability, 2026, pp. 2999–3023, doi:<a href="https://doi.org/10.3150/26-bej1976">10.3150/26-bej1976</a>.
  short: O. Kolupaiev, Bernoulli 32 (2026) 2999–3023.
corr_author: '1'
das_tickbox: '0'
date_created: 2026-10-12T12:04:45Z
date_published: 2026-11-01T00:00:00Z
date_updated: 2026-10-14T07:34:08Z
day: '01'
department:
- _id: LaEr
doi: 10.3150/26-bej1976
ec_funded: 1
external_id:
  arxiv:
  - '2503.21472'
fulldoi: https://doi.org/10.3150/26-bej1976
intvolume: '        32'
issue: '4'
keyword:
- correlated random matrix
- eigenvalue perturbation theory
- Local law
- Wigner-type matrix
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2503.21472
month: '11'
oa: 1
oa_version: Preprint
page: 2999-3023
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Bernoulli
publication_identifier:
  issn:
  - 1350-7265
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Spectral independence of almost fully correlated random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 32
year: '2026'
...