Duke Mathematical Journal

Localization for the random displacement model

Frédéric Klopp, Michael Loss, Shu Nakamura, and Günter Stolz

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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.”

Article information

Source
Duke Math. J., Volume 161, Number 4 (2012), 587-621.

Dates
First available in Project Euclid: 1 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1330610808

Digital Object Identifier
doi:10.1215/00127094-1548353

Mathematical Reviews number (MathSciNet)
MR2891530

Zentralblatt MATH identifier
1285.82030

Subjects
Primary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Secondary: 47B80: Random operators [See also 47H40, 60H25]

Citation

Klopp, Frédéric; Loss, Michael; Nakamura, Shu; Stolz, Günter. Localization for the random displacement model. Duke Math. J. 161 (2012), no. 4, 587--621. doi:10.1215/00127094-1548353. https://projecteuclid.org/euclid.dmj/1330610808


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