TY - JOUR
AB - 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.
AU - Erdös, László
AU - Ji, Hong Chang
ID - 14667
IS - 4
JF - Annales de l'institut Henri Poincare (B) Probability and Statistics
SN - 0246-0203
TI - Functional CLT for non-Hermitian random matrices
VL - 59
ER -