Frequency dependence of Hölder continuity for quasiperiodic Schrödinger operators

Abstract

We study 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, and conclude that for almost all values of $\beta$, the density of states measure is not Hölder continuous.