---
res:
bibo_abstract:
- 'We consider large non-Hermitian random matrices X with complex, independent,
identically distributed centred entries and show that the linear statistics of
their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives.
Previously this result was known only for a few special cases; either the test
functions were required to be analytic [72], or the distribution of the matrix
elements needed to be Gaussian [73], or at least match the Gaussian up to the
first four moments [82, 56]. We find the exact dependence of the limiting variance
on the fourth cumulant that was not known before. The proof relies on two novel
ingredients: (i) a local law for a product of two resolvents of the Hermitisation
of X with different spectral parameters and (ii) a coupling of several weakly
dependent Dyson Brownian motions. These methods are also the key inputs for our
analogous results on the linear eigenvalue statistics of real matrices X that
are presented in the companion paper [32]. @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: 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: 10.1002/cpa.22028
bibo_issue: '5'
bibo_volume: 76
dct_date: 2023^xs_gYear
dct_identifier:
- UT:000724652500001
dct_isPartOf:
- http://id.crossref.org/issn/0010-3640
- http://id.crossref.org/issn/1097-0312
dct_language: eng
dct_publisher: Wiley@
dct_title: Central limit theorem for linear eigenvalue statistics of non-Hermitian
random matrices@
...