Anderson localization and Hölder continuity of the integrated density of states for analytic quasiperiodic Schrödinger operators

We establish both Anderson localization and Hölder continuity of the integrated density of states for quasiperiodic Schrödinger operators on ${\mathbb{Z}}^d$ with any non-constant analytic potential and any Diophantine frequency in the perturbative regime. Our proof is based on a new method for controlling Green’s functions and eliminating double resonances, in the spirit of multi-scale analysis. To the best of our knowledge, this is the first multi-scale analysis approach that works for fixed Diophantine frequencies and potentials beyond the cosine type.