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.