Localization and mobility edge for sparsely random potentials
  In this paper we consider sparsely random potentials in 5 or more dimensional cubic lattice and exhibit localized and extended states. We identify also the mobility edge for a class of potentials going to infinity at infinity. Our treatment includes a large class of unperturbed selfadjoint opeartors commuting with the usual Laplacian on the lattice. 
M Krishna, J Obermeit