Density of States under non-local interactions II. Simplified polynomially screened interactions

Following [5], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with infinite-range interactions. In the present work, we study in detail a class of polynomially decaying interaction potentials of rather artificial (piecewise-constant) form, and give a complete proof of infinite smoothness of the IDS in an arbitrarily large finite domain subject to the fluctuations of the entire, infinite random environment. A variant of this result, based as in [5] on the harmonic analysis of probability measures, results in a proof of spectral and dynamical Anderson localization in the considered models.