Mesoscopic central limit theorem for non-Hermitian random matrices Cipolloni, Giorgio ; https://orcid.org/0000-0002-4901-7992 Erdös, László ; https://orcid.org/0000-0001-5366-9603 Schröder, Dominik J ; https://orcid.org/0000-0002-2904-1856 We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0<a<1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a=0 , to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator. Springer Nature 2024 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/14408 Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2024;188:1131-1182. doi:<a href="https://doi.org/10.1007/s00440-023-01229-1">10.1007/s00440-023-01229-1</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00440-023-01229-1 info:eu-repo/semantics/altIdentifier/issn/0178-8051 info:eu-repo/semantics/altIdentifier/e-issn/1432-2064 info:eu-repo/semantics/altIdentifier/wos/001118972500001 info:eu-repo/semantics/altIdentifier/arxiv/2210.12060 info:eu-repo/semantics/openAccess