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Fluctuations and growth of the magnitude of the Dirichlet determinants of Anderson Model at all disorders

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Mathematics and Physics of Anderson localization: 50 Years After

We consider the Schrodinger operator of the Anderson model in a quasi-one-dimensional domain with Dirichlet boundary condition. We show the exponential growth of the characteristic determinant of the problem. In particular, we give an effective, finite number of factors lower bound for the upper Lyapunov exponent of the product of the corresponding symplectic matrices. We explain the mechanism responsible for exponentially large magnitude of the Dirichlet determinant. The central part of this mechanism consists of the fact that the logarithm of the determinant has large fluctuations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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