@article{14667,
abstract = {For large dimensional non-Hermitian random matrices X with real or complex independent, identically distributed, centered entries, we consider the fluctuations of f (X) as a matrix where f is an analytic function around the spectrum of X. We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits Gaussian fluctuations as the matrix size grows to infinity, which consists of two independent modes corresponding to the tracial and traceless parts of A. We find a new formula for the variance of the traceless part that involves the Frobenius norm of A and the L2-norm of f on the boundary of the limiting spectrum. },
author = {Erdös, László and Ji, Hong Chang},
issn = {0246-0203},
journal = {Annales de l'institut Henri Poincare (B) Probability and Statistics},
number = {4},
pages = {2083--2105},
publisher = {Institute of Mathematical Statistics},
title = {{Functional CLT for non-Hermitian random matrices}},
doi = {10.1214/22-AIHP1304},
volume = {59},
year = {2023},
}