---
res:
  bibo_abstract:
  - 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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Giorgio
      foaf_name: Cipolloni, Giorgio
      foaf_surname: Cipolloni
      foaf_workInfoHomepage: http://www.librecat.org/personId=42198EFA-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-4901-7992
  - foaf_Person:
      foaf_givenName: László
      foaf_name: Erdös, László
      foaf_surname: Erdös
      foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0001-5366-9603
  - foaf_Person:
      foaf_givenName: Sven Joscha
      foaf_name: Henheik, Sven Joscha
      foaf_surname: Henheik
      foaf_workInfoHomepage: http://www.librecat.org/personId=31d731d7-d235-11ea-ad11-b50331c8d7fb
    orcid: 0000-0003-1106-327X
  - foaf_Person:
      foaf_givenName: Dominik J
      foaf_name: Schröder, Dominik J
      foaf_surname: Schröder
      foaf_workInfoHomepage: http://www.librecat.org/personId=408ED176-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-2904-1856
  bibo_doi: 10.1016/j.jfa.2024.110495
  bibo_issue: '4'
  bibo_volume: 287
  dct_date: 2024^xs_gYear
  dct_identifier:
  - UT:001325502400001
  dct_isPartOf:
  - http://id.crossref.org/issn/0022-1236
  - http://id.crossref.org/issn/1096-0783
  dct_language: eng
  dct_publisher: Elsevier@
  dct_title: Optimal lower bound on eigenvector overlaps for non-Hermitian random
    matrices@
...