Asymptotic ergodicity of the eigenvalues of random operators in the localized phase
Spectral Theory
2011-05-25 v2 Mathematical Physics
math.MP
Probability
Abstract
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.
Keywords
Cite
@article{arxiv.1012.0831,
title = {Asymptotic ergodicity of the eigenvalues of random operators in the localized phase},
author = {Frédéric Klopp},
journal= {arXiv preprint arXiv:1012.0831},
year = {2011}
}
Comments
Various typos have been corrected