Weak Hölder continuity of Lyapunov exponent for Gevrey quasi-periodic Schrödinger cocycles

We prove the large deviation theorem (LDT) for quasi-periodic dynamically defined Gevrey Schrödinger cocycles with weak Liouville frequency. We show that the associated Lyapunov exponent is log-Hölder continuous, while the frequency satisfies \beta(\omega) = 0 .