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An extension of Kotani's theorem to random generalized Sturm-Liouville operators

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Abstract

We consider the random operator: −d/m ω(dx)d +/dx+q ω(x), wherem ω(dx) andq ω(x) are a stationary ergodic random measure and a random function respectively. To this general case, we extend Kotani's theorem which asserts that the absolutely continuous spectrum is completely determined by the Ljapounov indices. Our framework includes the case of stochastic Jacobi matrices treated by Simon.

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Communicated by B. Simon

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Minami, N. An extension of Kotani's theorem to random generalized Sturm-Liouville operators. Commun.Math. Phys. 103, 387–402 (1986). https://doi.org/10.1007/BF01211754

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  • DOI: https://doi.org/10.1007/BF01211754

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