Kyoto Journal of Mathematics

Generalized eigenvalue-counting estimates for some random acoustic operators

Yoshihiko Kitagaki

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For some discrete random acoustic operators, we prove Wegner estimates. These estimates are applied to show some regularity of the integrated density of states. Moreover, we prove the generalized eigenvalue-counting estimates by using Combes, Germinet, and Klein’s method. As an application, the multiplicity of the eigenvalues in some interval where the Anderson localization occurs is proven to be finite. For certain models, Poisson statistics for eigenvalues and Lifshitz tails are also studied.

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Kyoto J. Math., Volume 51, Number 2 (2011), 439-465.

First available in Project Euclid: 22 April 2011

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Zentralblatt MATH identifier

Primary: 47B80: Random operators [See also 47H40, 60H25] 60H25: Random operators and equations [See also 47B80]


Kitagaki, Yoshihiko. Generalized eigenvalue-counting estimates for some random acoustic operators. Kyoto J. Math. 51 (2011), no. 2, 439--465. doi:10.1215/21562261-1214402.

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