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        <dc:title>Mesoscopic central limit theorem for non-Hermitian random matrices</dc:title>
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        <bibo:abstract>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&lt;a&lt;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.</bibo:abstract>
        <bibo:volume>188</bibo:volume>
        <bibo:startPage>1131-1182</bibo:startPage>
        <bibo:endPage>1131-1182</bibo:endPage>
        <dc:publisher>Springer Nature</dc:publisher>
        <bibo:doi rdf:resource="10.1007/s00440-023-01229-1" />
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