Asymptotic ergodicity of the eigenvalues of random operators in the localized phase
Résumé
We prove that, for a general class of random operators, the family of the unfolded eigenvalues in the localization region is asymptotically ergodic in the sense of N. Minami (see [Mi:11]). N. Minami conjectured this to be the case for discrete Anderson model in the localized regime. We also provide a local analogue of this result. From the asymptotics ergodicity, one can recover the statistics of the level spacings as well as a number of other spectral statistics. Our proofs rely on the analysis developed in http://arxiv.org/abs/1011.1832.
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|