Holder regularity of integrated density of states for the Almost Mathieu operator in a perturbative regime

Consider the Almost Mathieu operator H-lambda = lambda cos 2 pi(k omega +theta)+Delta on the lattice. It is shown that for large lambda, the integrated density of states is Holder continuous of exponent kappa < 1/2. This result gives a precise version in the perturbative regime of recent work by M. Goldstein and W. Schlag on Holder regularity of the integrated density of states for 1D quasi-periodic lattice Schrodinger operators, assuming positivity of the Lyapunov exponent (and proven by different means). Our approach provides also a new way to control Green's functions, in the spirit of the author's work in KAM theory. It is by no means restricted to the cosine-potential and extends to band operators.