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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2007

1/fα noise in the fluctuations of the spectra of tridiagonal random matrices from the beta-Hermite ensemble

Camille Male
Gérard Le Caër

Résumé

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

Dates et versions

hal-00905631 , version 1 (18-11-2013)

Identifiants

Citer

Camille Male, Gérard Le Caër, Renaud Delannay. 1/fα noise in the fluctuations of the spectra of tridiagonal random matrices from the beta-Hermite ensemble. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2007, 76 (4), pp.042101. ⟨10.1103/PhysRevE.76.042101⟩. ⟨hal-00905631⟩
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