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Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase

Frédéric Klopp (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in [12]. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of [10]. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues covariantly...

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