2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58173In 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.Completely revised, main theorems modified; latex2e fileMathematical PhysicsDisordered Systems and Neural NetworksSpectral Theory81Q10; 47B80text