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Mesoscopic eigenvalue statistics for correlated random matrices

Probability 2026-07-07 v1

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.

Cite

@article{arxiv.2607.05848,
  title  = {Mesoscopic eigenvalue statistics for correlated random matrices},
  author = {László Erdős and Jaehun Lee},
  journal= {arXiv preprint arXiv:2607.05848},
  year   = {2026}
}

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44 pages