We establish sharp results on the modulus of continuity distribution spectral measure for multi-frequency Schrodinger operators with Diphantine frequencies and small analytic potentials.

Given a hyperbolic homeomorphism on compact metric space, consider the space of linear cocycles over this base dynamics which are Hölder continuous and whose projective actions partially dynamical systems. We prove that locally near any typical cocycle, Lyapunov exponents functions relative to uniform topology. This result is obtained as consequence large deviations type estimate in cocycles. A...