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Generalized eigenvalue-counting estimates for some random acoustic operators. (English) Zbl 1242.47031

In this paper, the author proves a Wegner estimate and a generalized eigenvalue counting estimate for some discrete random acoustic operators. The Wegner estimate is applied to obtain some regularity of the integrated density of states. By means of the generalized eigenvalue counting estimate, the author establishes that the multiplicity of the eigenvalues in some interval where the Anderson localization occurs, is finite. Moreover, for certain models, Poisson statistics for eigenvalues and Lifshitz tails are also investigated.

MSC:

47B80 Random linear operators
60H25 Random operators and equations (aspects of stochastic analysis)
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
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