Tags → #clt

Fluctuations of functions of Wigner matrices
We prove a CLT for the entrywise fluctuations of functions of random matrices. The use of Pleijel's formula makes our result applicable to all functions of bounded variation.

Functional central limit theorems for Wigner matrices
We extend the classical CLTs for linear statistics functionally, in the sense that we prove the CLT for traces auf functions of Wigner matrices multiplied with arbitrary deterministic observables.

Mesoscopic central limit theorem for nonHermitian random matrices
We extend our previous result on the CLT for the linear statistics of IID random matrices to the entire mesoscopic regime.