Abstract
The purpose of the present work is to establish decorrelation estimates for the eigenvalues of the discrete Anderson model localized near two distinct energies inside the localization region. In dimension one, we prove these estimates at all energies. In higher dimensions, the energies are required to be sufficiently far apart from each other. As a consequence of these decorrelation estimates, we obtain the independence of the limits of the local level statistics at two distinct energies.
Résumé
Dans ce travail, nous établissons des inégalités de décorrélation pour les valeurs propres proches de deux énergies distinctes. En dimension 1, nous démontrons que ces inégalités sont vraies quel que soit le choix de ces deux énergies. En dimension supérieure, il nous faut supposer que les deux énergies sont suffisamment éloignées l’une de l’autre. Comme conséquence de ces inégalités de décorrélation, nous démontrons que les limites des statistiques locales des valeurs propres sont indépendantes pour deux énergies distinctes.
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Communicated by B. Simon
The author is supported by the grant ANR-08-BLAN-0261-01.
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Klopp, F. Decorrelation Estimates for the Eigenlevels of the Discrete Anderson Model in the Localized Regime. Commun. Math. Phys. 303, 233–260 (2011). https://doi.org/10.1007/s00220-011-1203-3
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DOI: https://doi.org/10.1007/s00220-011-1203-3