Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices

Yiting Li, Kevin Schnelli, Yuanyuan Xu

We consider $N$ by $N$ deformed Wigner random matrices of the form $X_N=H_N+A_N$, where $H_N$ is a real symmetric or complex Hermitian Wigner matrix and $A_N$ is a deterministic re…