<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:msup><mml:mi>f</mml:mi><mml:mi>α</mml:mi></mml:msup></mml:mrow></mml:math>noise in the fluctuations of the spectra of tridiagonal random matrices from the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>-Hermite ensemble

TL;DRAbstract

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.

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