Frequency dependence of H\"older continuity for quasiperiodic Schr\"odinger operators

Abstract

We prove estimates on the H\"older exponent of the density of states measure for discrete Schr\"odinger 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 H\"older continuous.