Localization in One Dimension

It was first claimed by P.W. Anderson (1958) in [8] for the multidimensional random Schrödinger operator on a lattice, (associated with i.i.d. potentials) that the spectrum ought to be pure point with exponentially decaying eigenfunctions for a “typical sample” and for “large disorder”. It was later conjectured by Mott & Twose in [249] that this property should hold in the one dimensional case at any disorder. This chapter is devoted to the proof of this last conjecture which we will extend to quasi-one dimensional systems.