Hölder continuity of the integrated density of states for Liouville frequencies

We prove Hölder continuity of the Lyapunov exponent $L(\omega ,E)$ and the integrated density of states at energies that satisfy $L(\omega ,E)>4\kappa (\omega ,E)\cdot \beta (\omega )\ge 0$ for general analytic potentials, with $\kappa (\omega ,E)$ being Avila’s acceleration.