preprint submitted Jaehun Lee author 96155047-f36a-11ef-b766-8b5ae7cecd49 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 LaEr department Random matrices beyond Wigner-Dyson-Mehta project We prove a mesoscopic central limit theorem for linear eigenvalue statistics of correlated Hermitian random matrices. The class considered here includes Wigner and Wigner-type matrices, as well as models whose entry correlations decay polynomially in the distance between index pairs. The proof combines a multivariate cumulant expansion with multi-resolvent local laws and a detailed analysis of the resulting variance kernel on the operator-level. 2026 eng Central limit theoremuniversalitymatrix Dyson equationmulti-resolvent local law 2607.0584810.48550/arXiv.2607.05848 Lee J, Erdös L. Mesoscopic eigenvalue statistics for correlated random matrices. 2607.05848. Lee, Jaehun, and László Erdös. “Mesoscopic Eigenvalue Statistics for Correlated Random Matrices,” n.d. <a href="https://doi.org/10.48550/arXiv.2607.05848">https://doi.org/10.48550/arXiv.2607.05848</a>. Lee J, Erdös L. Mesoscopic eigenvalue statistics for correlated random matrices. doi:<a href="https://doi.org/10.48550/arXiv.2607.05848">10.48550/arXiv.2607.05848</a> J. Lee and L. Erdös, “Mesoscopic eigenvalue statistics for correlated random matrices.” . Lee, J., &#38; Erdös, L. (n.d.). Mesoscopic eigenvalue statistics for correlated random matrices. <a href="https://doi.org/10.48550/arXiv.2607.05848">https://doi.org/10.48550/arXiv.2607.05848</a> Lee, Jaehun, and László Erdös. <i>Mesoscopic Eigenvalue Statistics for Correlated Random Matrices</i>. 2607.05848, doi:<a href="https://doi.org/10.48550/arXiv.2607.05848">10.48550/arXiv.2607.05848</a>. J. Lee, L. Erdös, (n.d.). 223592026-07-18T08:59:02Z2026-07-20T10:55:10Z