Mesoscopic eigenvalue statistics for correlated random matrices
Lee J, Erdös L. Mesoscopic eigenvalue statistics for correlated random matrices. 2607.05848.
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Abstract
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.
Publishing Year
Date Published
2026-07-07
Acknowledgement
Supported by ERC Advanced Grant “RMTBeyond” No. 101020331
Article Number
2607.05848
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Cite this
Lee J, Erdös L. Mesoscopic eigenvalue statistics for correlated random matrices. doi:10.48550/arXiv.2607.05848
Lee, J., & Erdös, L. (n.d.). Mesoscopic eigenvalue statistics for correlated random matrices. https://doi.org/10.48550/arXiv.2607.05848
Lee, Jaehun, and László Erdös. “Mesoscopic Eigenvalue Statistics for Correlated Random Matrices,” n.d. https://doi.org/10.48550/arXiv.2607.05848.
J. Lee and L. Erdös, “Mesoscopic eigenvalue statistics for correlated random matrices.” .
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. 2607.05848, doi:10.48550/arXiv.2607.05848.
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