Fractional Moment Estimates for Random Unitary Operators |
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Authors: | Alain Joye |
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Institution: | (1) Institut Fourier, Université de Grenoble 1, BP 74, F-38402, Saint-Martin d Hères Cedex, France |
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Abstract: | We consider unitary analogs of d-dimensional Anderson models on l2( $$\mathbb(z)$$d) defined by the product U =D S where S is a deterministic unitary and D is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman–Molchanov to get exponential estimates on fractional moments of the matrix elements of U (U –z)–1, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of S. Such estimates imply almost sure localization for U . |
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Keywords: | fractional moment method unitary operators localization |
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