---
res:
bibo_abstract:
- We extend our recent result [22] on the central limit theorem for the linear eigenvalue
statistics of non-Hermitian matrices X with independent, identically distributed
complex entries to the real symmetry class. We find that the expectation and variance
substantially differ from their complex counterparts, reflecting (i) the special
spectral symmetry of real matrices onto the real axis; and (ii) the fact that
real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously
known special cases where either the test function is analytic [49] or the first
four moments of the matrix elements match the real Gaussian [59, 44]. The key
element of the proof is the analysis of several weakly dependent Dyson Brownian
motions (DBMs). The conceptual novelty of the real case compared with [22] is
that the correlation structure of the stochastic differentials in each individual
DBM is non-trivial, potentially even jeopardising its well-posedness.@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: 10.1214/21-EJP591
bibo_volume: 26
dct_date: 2021^xs_gYear
dct_identifier:
- UT:000641855600001
dct_isPartOf:
- http://id.crossref.org/issn/10836489
dct_language: eng
dct_publisher: Institute of Mathematical Statistics@
dct_title: Fluctuation around the circular law for random matrices with real entries@
...