Kyoto Journal of Mathematics

Generalized eigenvalue-counting estimates for some random acoustic operators

Yoshihiko Kitagaki

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 22 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1303494509

Digital Object Identifier
doi:10.1215/21562261-1214402

Mathematical Reviews number (MathSciNet)
MR2793274

Zentralblatt MATH identifier
1242.47031

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

Citation

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. https://projecteuclid.org/euclid.kjm/1303494509


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