Michael Goldstein, Wilhelm Schlag, Hölder Continuity of the Integrated Density of States for Quasi-Periodic Schrödinger Equations and Averages of Shifts of Subharmonic Functions, Annals of Mathematics, Second Series, Vol. 154, No. 1 (Jul., 2001), pp. 155-203
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Goldstein et al. (2001) studied this question.
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