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Global multiplicity bounds and spectral statistics for random operators
A. Mallick,
Published in World Scientific
Volume: 32
Issue: 9
In this paper, we consider Anderson type operators on a separable Hilbert space where the random perturbations are finite rank and the random variables have full support on . We show that spectral multiplicity has a uniform lower bound whenever the lower bound is given on a set of positive Lebesgue measure on the point spectrum away from the continuous one. We also show a deep connection between the multiplicity of pure point spectrum and local spectral statistics, in particular, we show that spectral multiplicity higher than one always gives non-Poisson local statistics in the framework of Minami theory. In particular, for higher rank Anderson models with pure point spectrum, with the randomness having support equal to , there is a uniform lower bound on spectral multiplicity and in case this is larger than one, the local statistics is not Poisson. © 2020 World Scientific Publishing Company.
About the journal
JournalReviews in Mathematical Physics
PublisherWorld Scientific