Asymptotic ergodicity of the eigenvalues of random operators in the localized phase

Frédéric Klopp (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: random operators; localization; level statistics

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Probabilités [math.PR]

Frédéric Klopp. Asymptotic ergodicity of the eigenvalues of random operators in the localized phase. 2011. ⟨hal-00542881v2⟩