Functional central limit theorems for Wigner matrices
Functional central limit theorems for Wigner matrices
We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f(W). Going beyond the well-studied tracial mode, Trf(W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf(W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. …