Central limit theorem for mesoscopic eigenvalue statistics of the free sum of matrices

Zhigang Bao, Kevin Schnelli, Yuanyuan Xu

We consider random matrices of the form $H_N=A_N+U_N{B}_N{U}_N^{\ast }$, where $A_N$, $B_N$ are two $N$ by $N$ deterministic Hermitian matrices and $U_N$ is a Haar distributed random unita…