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- W3000983880 abstract "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 [Formula: see text]. 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 [Formula: see text], there is a uniform lower bound on spectral multiplicity and in case this is larger than one, the local statistics is not Poisson." @default.
- W3000983880 created "2020-01-30" @default.
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- W3000983880 date "2020-02-13" @default.
- W3000983880 modified "2023-09-27" @default.
- W3000983880 title "Global multiplicity bounds and spectral statistics for random operators" @default.
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- W3000983880 doi "https://doi.org/10.1142/s0129055x20500257" @default.
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