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We study the density of states measure for some class of random unitary bandmatrices and prove a Thouless formula relating it to the associated Lyapunovexponent. This class of random matrices appears in the study of the dynamicalstability of certain quantum systems and can also be considered as a unitaryversion of the Anderson model. We further determine the support of the densityof states measure and provide a condition ensuring it possesses an analyticdensity

Density of States and Thouless Formula for Random Unitary Band Matrices