Uniform Anderson Localization and Non-local Minami-type Estimates in Limit-periodic Media
2023, v.29, Issue 4, 549-571
We prove a uniform exponential localization of eigenfunctions and simplicity of spectrum for a class
of limit-periodic lattice Schrodinger 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.
Keywords: Anderson localization; limit-periodic potentials; Minami estimates