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Boosted Simon-Wolff Spectral Criterion and Resonant Delocalization

Author(s): Aizenman, Michael; Warzel, Simone

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Abstract: Discussed here are criteria for the existence of continuous components in the spectra of operators with random potential. First, the essential condition for the Simon-Wolff criterion is shown to be measurable at infinity. By implication, for the i.i.d. case and more generally potentials with the K-property, the criterion is boosted by a zero-one law. The boosted criterion, combined with tunneling estimates, is then applied for sufficiency conditions for the presence of continuous spectrum for random Schrodinger operators. The general proof strategy that this yields is modeled on the resonant delocalization arguments by which continuous spectrum in the presence of disorder was previously established for random operators on tree graphs. In another application of the Simon-Wolff rank-one analysis we prove the almost sure simplicity of the pure point spectrum for operators with random potentials of conditionally continuous distribution.(c) 2015 Wiley Periodicals, Inc.
Publication Date: Nov-2016
Electronic Publication Date: 15-Dec-2015
Citation: Aizenman, Michael, Warzel, Simone. (2016). Boosted Simon-Wolff Spectral Criterion and Resonant Delocalization. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 69 (2195 - 2218. doi:10.1002/cpa.21625
DOI: doi:10.1002/cpa.21625
ISSN: 0010-3640
EISSN: 1097-0312
Pages: 2195 - 2218
Type of Material: Journal Article
Version: Author's manuscript

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