Uniform Anderson Localization and Non-local Minami-type Estimates in Limit-periodic Media

We prove a uniform exponential localization of eigenfunctions and simplicity of spectrum for a class of limit -periodic lattice Schr delta dinger operators. An important ingredient of the proof is a generalized variant of the well-known Minami estimates (correlation inequalities for the eigenvalues) to the case where the spectral intervals can be arbitrarily placed in the real line. The new correlation inequalities allow us to substantially simplify and make more transparent the application of the KAM (Kolmogorov-Arnold-Moser) techniques.