15 March 2012 Localization for the random displacement model
Frédéric Klopp, Michael Loss, Shu Nakamura, Günter Stolz
Duke Math. J. 161(4): 587-621 (15 March 2012). DOI: 10.1215/00127094-1548353

Abstract

We prove spectral and dynamical localization for the multidimensional random displacement model near the bottom of its spectrum by showing that the approach through multiscale analysis is applicable. In particular, we show that a previously known Lifshitz tail bound can be extended to our setting and prove a new Wegner estimate. A key tool is given by a quantitative form of a property of a related single-site Neumann problem which can be described as “bubbles tend to the corners.”

Citation

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Frédéric Klopp. Michael Loss. Shu Nakamura. Günter Stolz. "Localization for the random displacement model." Duke Math. J. 161 (4) 587 - 621, 15 March 2012. https://doi.org/10.1215/00127094-1548353

Information

Published: 15 March 2012
First available in Project Euclid: 1 March 2012

zbMATH: 1285.82030
MathSciNet: MR2891530
Digital Object Identifier: 10.1215/00127094-1548353

Subjects:
Primary: 82B44
Secondary: 47B80

Rights: Copyright © 2012 Duke University Press

Vol.161 • No. 4 • 15 March 2012
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