---
OA_place: repository
OA_type: green
_id: '22923'
abstract:
- lang: eng
  text: "We study the sensitivity of the eigenvectors of random matrices, showing
    that even small perturbations make the eigenvectors almost orthogonal. More precisely,
    we consider two deformed Wigner matrices \U0001D44A +\U0001D4371, \U0001D44A +\U0001D4372
    and show that their bulk eigenvectors become asymptotically orthogonal as soon
    as Tr⁡(\U0001D4371−\U0001D4372)2 ≫1, or their respective energies are separated
    on a scale much bigger than the local eigenvalue spacing. Furthermore, we show
    that quadratic forms of eigenvectors of \U0001D44A +\U0001D4371, \U0001D44A +\U0001D4372
    with any deterministic matrix \U0001D434 ∈\U0001D402\U0001D441×\U0001D441 in a
    specific subspace of codimension one are of size \U0001D441−1/2. This proves a
    generalization of the eigenstate thermalization hypothesis to eigenvectors belonging
    to two different spectral families."
acknowledgement: L. Erdős, J. Henheik and O. Kolupaiev were supported by the ERC Advanced
  Grant “RMTBeyond” No. 101020331. G. Cipolloni is partially supported by the MUR
  Excellence Department Project MatMod@TOV awarded to the Department of Mathematics,
  University of Rome Tor Vergata, CUP E83C18000100006.
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: 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: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for
    random matrices. <i>Annals of Applied Probability</i>. 2026;36(4):3707-3756. doi:<a
    href="https://doi.org/10.1214/26-AAP2318">10.1214/26-AAP2318</a>
  apa: Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2026). Eigenvector
    decorrelation for random matrices. <i>Annals of Applied Probability</i>. Institute
    of Mathematical Statistics. <a href="https://doi.org/10.1214/26-AAP2318">https://doi.org/10.1214/26-AAP2318</a>
  chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev.
    “Eigenvector Decorrelation for Random Matrices.” <i>Annals of Applied Probability</i>.
    Institute of Mathematical Statistics, 2026. <a href="https://doi.org/10.1214/26-AAP2318">https://doi.org/10.1214/26-AAP2318</a>.
  ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation
    for random matrices,” <i>Annals of Applied Probability</i>, vol. 36, no. 4. Institute
    of Mathematical Statistics, pp. 3707–3756, 2026.
  ista: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2026. Eigenvector decorrelation
    for random matrices. Annals of Applied Probability. 36(4), 3707–3756.
  mla: Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.”
    <i>Annals of Applied Probability</i>, vol. 36, no. 4, Institute of Mathematical
    Statistics, 2026, pp. 3707–56, doi:<a href="https://doi.org/10.1214/26-AAP2318">10.1214/26-AAP2318</a>.
  short: G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Annals of Applied Probability
    36 (2026) 3707–3756.
corr_author: '1'
das_tickbox: '0'
date_created: 2026-09-13T22:01:54Z
date_published: 2026-08-01T00:00:00Z
date_updated: 2026-09-16T10:00:54Z
day: '01'
department:
- _id: LaEr
- _id: GradSch
doi: 10.1214/26-AAP2318
ec_funded: 1
external_id:
  arxiv:
  - '2410.10718'
fulldoi: https://doi.org/10.1214/26-AAP2318
intvolume: '        36'
issue: '4'
keyword:
- characteristic flow
- Davis–Kahan theorem
- Eigenstate thermalization
- Eigenvector perturbation theory
- Local law
- zigzag strategy
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2410.10718
mathsc:
- 60B20
- 82C10
month: '08'
oa: 1
oa_version: Preprint
page: 3707-3756
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Annals of Applied Probability
publication_identifier:
  issn:
  - 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
  record:
  - id: '19546'
    relation: earlier_version
    status: public
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Eigenvector decorrelation for random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2026'
...