---
res:
bibo_abstract:
- We consider N×N non-Hermitian random matrices of the form X+A, where A is a general
deterministic matrix and N−−√X consists of independent entries with zero mean,
unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner
estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1) and
(ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1);
both results are optimal up to the factor No(1). The latter result complements
the very recent matching lower bound obtained in [15] (arXiv:2301.03549) and improves
the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819, arXiv:2005.08930,
arXiv:2005.08908). Our main ingredient, a near-optimal lower tail estimate for
the small singular values of X+A−z, is of independent interest.@eng
bibo_authorlist:
- 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: Hong Chang
foaf_name: Ji, Hong Chang
foaf_surname: Ji
foaf_workInfoHomepage: http://www.librecat.org/personId=dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
bibo_doi: 10.1002/cpa.22201
dct_date: 2024^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0010-3640
- http://id.crossref.org/issn/1097-0312
dct_language: eng
dct_publisher: Wiley@
dct_title: Wegner estimate and upper bound on the eigenvalue condition number of
non-Hermitian random matrices@
...