 04395 Alain Joye
 Fractional Moment Estimates for Random Unitary Operators
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Nov 21, 04

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Abstract. We consider unitary analogs of $d$dimensional Anderson
models on $l^2(\Z^d)$ defined by the product $U_\omega=D_\omega S$
where $S$ is a deterministic unitary and $D_\omega$ 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 offdiagonal elements. We adapt the method of AizenmanMolchanov to get exponential estimates on fractional moments of the matrix elements of $U_\omega(U_\omega z)^{1}$, provided the distribution of phases is absolutely continuous and the parameters correspond to small offdiagonal elements of $S$. Such estimates imply almost sure localization for $U_\omega$.
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