Fractional Moment Estimates for Random Unitary Operators
نویسنده
چکیده
We consider unitary analogs of d−dimensional Anderson models on l2(Zd) defined by the product Uω = DωS where S is a deterministic unitary and Dω 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 Uω(Uω − 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 Uω.
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