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Localization for Random Block Operators

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Mathematical Physics, Spectral Theory and Stochastic Analysis

Part of the book series: Operator Theory: Advances and Applications ((APDE,volume 232))

Abstract

We continue the investigations of Kirsch, Metzger and the secondnamed author [J. Stat. Phys. 143, 1035–1054 (2011)] on spectral properties of a certain type of random block operators. In particular, we establish an alternative version of a Wegner estimate and an improved result on Lifschitz tails at the internal band edges. Using these ingredients and the bootstrap multi-scale analysis, we also prove dynamical localization in a neighbourhood of the internal band edges.

Mathematics Subject Classification (2010). 47B80, 47A75.

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Correspondence to Martin Gebert .

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Dedicated to Michael Demuth on the occasion of his 65th birthday

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Gebert, M., Müller, P. (2013). Localization for Random Block Operators. In: Demuth, M., Kirsch, W. (eds) Mathematical Physics, Spectral Theory and Stochastic Analysis. Operator Theory: Advances and Applications(), vol 232. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0591-9_4

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