Scattering from Sparse Potentials on Graphs - Poulin, Ph. (Журнал математичної фізики, аналізу, геометрії, 2008)
We study the spectral structure of Schrödinger 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. Mathematics Subject Classification: 81Q10, 47B80.