2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103532We review some of the work by the authors on this topic. In particular, we discuss the recent paper "Fine properties of the IDS and a quantitative separation property of the Dirichlet eigenvalues".This article will appear in the proceedings to Yakov Grigoriewitch Sinai's 70th birthday conferenceMathematical Physics82B44, 39A70, 47B39, 47N55, 81Q10text