Duke Mathematical Journal
- Duke Math. J.
- Volume 161, Number 4 (2012), 587-621.
Localization for the random displacement model
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.”
Duke Math. J., Volume 161, Number 4 (2012), 587-621.
First available in Project Euclid: 1 March 2012
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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