Convergence of perturbation series for unbounded monotone quasiperiodic operators

We consider a class of unbounded quasiperiodic Schrödinger-type operators on ℓ2(Zd) with monotone potentials (akin to the Maryland model) and show that Rayleigh–Schrödinger perturbation series for these converges in regime small kinetic energies, uniformly spectrum. As consequence, we obtain new proof Anderson localization more general than before such operators, explicit convergent expansions eigenvalues eigenvectors. This result can be restricted an energy window if potential is only locally one-to-one. A modification this approach also allows non-strictly have flat segment, under additional restrictions frequencies.