Scattering from Sparse Potentials on Graphs

Abstract

We study the spectral structure of Schrodinger operators H = Δ+V for random potentials supported on sparse sets. In the past years examples of such operators whose spectra almost surely satisfy the following properties have been exhibited: Anderson localization holds outside spec(Δ), while the wave operators Ω⁺(H, Δ) exist inside this last set. We continue this program by presenting sparseness conditions under which Ω⁺(Δ, H) also exist.