---
OA_place: publisher
OA_type: hybrid
_id: '17049'
abstract:
- lang: eng
  text: We consider large non-Hermitian NxN matrices with an additive independent,
    identically distributed (i.i.d.) noise for each matrix elements. We show that
    already a small noise of variance 1/N completely thermalises the bulk singular
    vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity
    (QUE) with an optimal speed of convergence. In physics terms, we thus extend the
    Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and
    proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an
    i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal
    overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also
    known as the (square of the) eigenvalue condition number measuring the sensitivity
    of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment
    beyond the explicitly computable Ginibre ensemble apart from the very recent upper
    bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition
    of general observables in random matrix theory that governs the size of products
    of resolvents with deterministic matrices in between.
acknowledgement: "Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported
  by the SNSF Ambizione Grant PZ00P2_209089."
article_number: '110495'
article_processing_charge: Yes (via OA deal)
article_type: original
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: Dominik J
  full_name: Schröder, Dominik J
  id: 408ED176-F248-11E8-B48F-1D18A9856A87
  last_name: Schröder
  orcid: 0000-0002-2904-1856
citation:
  ama: Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector
    overlaps for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>.
    2024;287(4). doi:<a href="https://doi.org/10.1016/j.jfa.2024.110495">10.1016/j.jfa.2024.110495</a>
  apa: Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Schröder, D. J. (2024). Optimal
    lower bound on eigenvector overlaps for non-Hermitian random matrices. <i>Journal
    of Functional Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2024.110495">https://doi.org/10.1016/j.jfa.2024.110495</a>
  chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder.
    “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.”
    <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href="https://doi.org/10.1016/j.jfa.2024.110495">https://doi.org/10.1016/j.jfa.2024.110495</a>.
  ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower
    bound on eigenvector overlaps for non-Hermitian random matrices,” <i>Journal of
    Functional Analysis</i>, vol. 287, no. 4. Elsevier, 2024.
  ista: Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. 2024. Optimal lower bound on
    eigenvector overlaps for non-Hermitian random matrices. Journal of Functional
    Analysis. 287(4), 110495.
  mla: Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for
    Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>, vol. 287,
    no. 4, 110495, Elsevier, 2024, doi:<a href="https://doi.org/10.1016/j.jfa.2024.110495">10.1016/j.jfa.2024.110495</a>.
  short: G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional
    Analysis 287 (2024).
corr_author: '1'
date_created: 2024-05-26T22:00:57Z
date_published: 2024-08-15T00:00:00Z
date_updated: 2026-04-07T12:37:11Z
day: '15'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2024.110495
ec_funded: 1
external_id:
  isi:
  - '001325502400001'
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intvolume: '       287'
isi: 1
issue: '4'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '08'
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: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
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scopus_import: '1'
status: public
title: Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices
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  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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