ar X iv : 0 90 7 . 14 94 v 1 [ m at h - ph ] 9 J ul 2 00 9 Grand Ensembles of deterministic operators . II . Localization for generic ” haarsh ” potentials

We consider a class of families of deterministic random lattice Schrödinger operators with potentials depending upon an infinite number of parameters on an auxiliary measurable space. We prove Anderson localization for generic families in the strong disorder regime, using a variant of the Multi-Scale Analysis. In our model, the potential is generated by a function on a torus which is discontinuous (”harsh”) and constructed with the help of an expansion which reminds Haar’s wavelet expansions (but is not orthogonal), so we call such potentials ”haarsh”. A different approach, also using a parameter exclusion technique, has been used by Chan [Chan07] for one-dimensional lattice Schrödinger operators with quasi-periodic, single-frequency potential which was assumed to be of class C(S).