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Summer 2011 Generalized eigenvalue-counting estimates for some random acoustic operators
Yoshihiko Kitagaki
Kyoto J. Math. 51(2): 439-465 (Summer 2011). DOI: 10.1215/21562261-1214402


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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Yoshihiko Kitagaki. "Generalized eigenvalue-counting estimates for some random acoustic operators." Kyoto J. Math. 51 (2) 439 - 465, Summer 2011.


Published: Summer 2011
First available in Project Euclid: 22 April 2011

zbMATH: 1242.47031
MathSciNet: MR2793274
Digital Object Identifier: 10.1215/21562261-1214402

Primary: 47B80 , 60H25

Rights: Copyright © 2011 Kyoto University

Vol.51 • No. 2 • Summer 2011
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