---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20478'
abstract:
- lang: eng
  text: 'We consider the Wigner minor process, i.e. the eigenvalues of an N\times
    N Wigner matrix H^{(N)} together with the eigenvalues of all its n\times n minors,
    H^{(n)}, n\le N. The top eigenvalues of H^{(N)} and those of its immediate minor
    H^{(N-1)} are very strongly correlated, but this correlation becomes weaker for
    smaller minors H^{(N-k)} as k increases. For the GUE minor process the critical
    transition regime around k\sim N^{2/3} was analyzed by Forrester and Nagao (J.
    Stat. Mech.: Theory and Experiment, 2011) providing an explicit formula for the
    nontrivial joint correlation function. We prove that this formula is universal,
    i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis
    of the sub- and supercritical regimes both for eigenvalues and for the corresponding
    eigenvector overlaps, thus we prove the decorrelation transition in full generality.'
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria). Zhigang Bao Supported by Hong Kong RGC Grant GRF 16304724, NSFC12222121
  and NSFC12271475. László Erdős, Joscha Henheik and Oleksii Kolupaiev Supported by
  the ERC Advanced Grant “RMTBeyond” No. 101020331.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- 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: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Oleksii
  full_name: Kolupaiev, Oleksii
  id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
  last_name: Kolupaiev
  orcid: 0000-0003-1491-4623
citation:
  ama: Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Decorrelation transition
    in the Wigner minor process. <i>Probability Theory and Related Fields</i>. 2025.
    doi:<a href="https://doi.org/10.1007/s00440-025-01422-4">10.1007/s00440-025-01422-4</a>
  apa: Bao, Z., Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2025).
    Decorrelation transition in the Wigner minor process. <i>Probability Theory and
    Related Fields</i>. Springer Nature. <a href="https://doi.org/10.1007/s00440-025-01422-4">https://doi.org/10.1007/s00440-025-01422-4</a>
  chicago: Bao, Zhigang, Giorgio Cipolloni, László Erdös, Sven Joscha Henheik, and
    Oleksii Kolupaiev. “Decorrelation Transition in the Wigner Minor Process.” <i>Probability
    Theory and Related Fields</i>. Springer Nature, 2025. <a href="https://doi.org/10.1007/s00440-025-01422-4">https://doi.org/10.1007/s00440-025-01422-4</a>.
  ieee: Z. Bao, G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Decorrelation
    transition in the Wigner minor process,” <i>Probability Theory and Related Fields</i>.
    Springer Nature, 2025.
  ista: Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation
    transition in the Wigner minor process. Probability Theory and Related Fields.
  mla: Bao, Zhigang, et al. “Decorrelation Transition in the Wigner Minor Process.”
    <i>Probability Theory and Related Fields</i>, Springer Nature, 2025, doi:<a href="https://doi.org/10.1007/s00440-025-01422-4">10.1007/s00440-025-01422-4</a>.
  short: Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory
    and Related Fields (2025).
corr_author: '1'
date_created: 2025-10-16T13:10:26Z
date_published: 2025-09-20T00:00:00Z
date_updated: 2026-06-18T18:23:40Z
day: '20'
ddc:
- '500'
department:
- _id: LaEr
doi: 10.1007/s00440-025-01422-4
ec_funded: 1
external_id:
  arxiv:
  - '2503.06549'
  isi:
  - '001574640900001'
fulldoi: https://doi.org/10.1007/s00440-025-01422-4
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s00440-025-01422-4
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Probability Theory and Related Fields
publication_identifier:
  eissn:
  - 1432-2064
  issn:
  - 0178-8051
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Decorrelation transition in the Wigner minor process
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...