1∕fαnoise in the fluctuations of the spectra of tridiagonal random matrices from theβ-Hermite ensemble

Abstract

The 1/falpha noise displayed by the fluctuation of the n th unfolded eigenvalue, where n plays the role of a discrete time, was recently characterized for the classical Gaussian ensembles of NxN random matrices. It is investigated here for the beta-Hermite ensemble by wavelet analysis of Monte Carlo simulated series both as a function of beta and of N. When beta decreases from 1 to 0, for a given and large enough N, the evolution from a 1/f noise at beta=1 Gaussian orthogonal ensemble (GOE) to a 1/f2 noise at beta=0 Gaussian diagonal ensemble (GDE) is heterogeneous with a approximately 1/f2 noise at the finest scales and an approximately 1/f noise at the coarsest ones.