Global multiplicity bounds and spectral statistics for random operators.
In: Reviews in Mathematical Physics, Jg. 32 (2020-10-01), Heft 9, S. N.PAG- (21S.)
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Zugriff:
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 ℝ. 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 ℝ , there is a uniform lower bound on spectral multiplicity and in case this is larger than one, the local statistics is not Poisson. [ABSTRACT FROM AUTHOR]
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Titel: |
Global multiplicity bounds and spectral statistics for random operators.
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Autor/in / Beteiligte Person: | Mallick, Anish ; Maddaly, Krishna |
Zeitschrift: | Reviews in Mathematical Physics, Jg. 32 (2020-10-01), Heft 9, S. N.PAG- (21S.) |
Veröffentlichung: | 2020 |
Medientyp: | academicJournal |
ISSN: | 0129-055X (print) |
DOI: | 10.1142/S0129055X20500257 |
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