Hölder continuity of the integrated density of states for Liouville frequencies

Abstract

We prove Hölder continuity of the Lyapunov exponent $L(\ddot{I}‰,E)$ and the integrated density of states at energies that satisfy $L(\ddot{I}‰,E)>4\hat{I}º(\ddot{I}‰,E)\cdot {\hat{I}}^2(\ddot{I}‰)\ge 0$ for general analytic potentials, with $\hat{I}º(\ddot{I}‰,E)$ being Avila's acceleration.