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

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

2010-12-03

arxiv.org/abs/1012.0831v2

Mathematics

Spectral Theory

Various typos have been corrected

Scientific paper

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 abs/1011.1832.

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