Frequency dependence of Hölder continuity for quasiperiodic Schrödinger operators

Abstract

We prove estimates on the Hölder exponent of the density of states measure for discrete Schrödinger operators with potential of the form $V(n)=\lambda (\lfloor (n+1)\beta \rfloor -\lfloor n\beta \rfloor )$, with $\lambda$ large enough, and conclude that for almost all values of $\beta$, the density of states measure is not Hölder continuous.