  Following [7,8], 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 and arbitrary
nontrivial probability distributions of the site potentials. In the present
work, we study $2$-particle Anderson Hamiltonians on a lattice and prove
spectral and strong dynamical localization at low energies, with exponentially
decaying eigenfunctions, for a class of site potentials featuring a power-law
decay.
