--- 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@ ...