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Description

Random Schr\"odinger operators on strips can be described by transfer matrices. Considering their action on a certain compact flag manifold one can obtain formulas for the Lyapunov exponents in terms of the invariant measure. For a perturbative analysis we are multiplying the random disorder by a coupling constant $\lambda$. The random phase hypothesis is a statement about the convergence of the invariant measure on the flag manifold for $\lambda\to 0$. It states that the limit of the invariant measures converges to a natural Haar measure. If for $\lambda=0$ the transfer matrix has only elliptic channels we obtain convergence to a measure with smooth density w.r.t. this Haar measure. For the Wegner L-orbital model we obtain exactly the Haar measure. CU