article published yes Volodymyr Riabov author 1949f904-edfb-11eb-afb5-e2dfddabb93b GradSch department LaEr department Random matrices beyond Wigner-Dyson-Mehta project We prove a universal mesoscopic central limit theorem for linear eigenvalue statistics of a Wigner-type matrix inside the bulk of the spectrum with compactly supported twice continuously differentiable test functions. The main novel ingredient is an optimal local law for the two-point function $T(z,\zeta)$ and a general class of related quantities involving two resolvents at nearby spectral parameters. On établit un théorème limite central universel pour les statistiques linéaires mésoscopiques des valeurs propres d’une matrice de type Wigner au milieu du spectre, avec des fonctions de classe et à support compact. La principale nouveauté de cette approche est qu’elle repose sur une loi locale optimale pour la fonction à deux points $T(z,\zeta)$ , ainsi que pour une classe plus générale d’observables impliquant deux résolvantes évaluées en des paramètres proches. Institute of Mathematical Statistics2025 eng 0246-0203 2301.01712 00142795360000410.1214/23-AIHP1438 611129-154 Riabov, V. (2025). Mesoscopic eigenvalue statistics for Wigner-type matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/23-AIHP1438">https://doi.org/10.1214/23-AIHP1438</a> Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2025. <a href="https://doi.org/10.1214/23-AIHP1438">https://doi.org/10.1214/23-AIHP1438</a>. Riabov V. 2025. Mesoscopic eigenvalue statistics for Wigner-type matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 61(1), 129–154. Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 61, no. 1, Institute of Mathematical Statistics, 2025, pp. 129–54, doi:<a href="https://doi.org/10.1214/23-AIHP1438">10.1214/23-AIHP1438</a>. V. Riabov, “Mesoscopic eigenvalue statistics for Wigner-type matrices,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 61, no. 1. Institute of Mathematical Statistics, pp. 129–154, 2025. Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2025;61(1):129-154. doi:<a href="https://doi.org/10.1214/23-AIHP1438">10.1214/23-AIHP1438</a> V. Riabov, Annales de l’institut Henri Poincare (B) Probability and Statistics 61 (2025) 129–154. 151282024-03-20T09:41:04Z2025-05-19T13:54:31Z