Absolutely continuous spectrum for random operators on trees of finite cone type (Q351315)

The work analyzes a spectrum of Laplace type operator on a large class of tree systems, namely on trees of finite cone (periodic trees) and its stability under small random perturbations by a potential. The main result is that the corresponding spectrum is continuous and its arbitrary large parts are stable if the perturbation potential is sufficiently small. The proof is based on the consideration of continuity of the Green function of the perturbed operator and the application of the contraction procedure. The obtained results relate to the physical background knows as the Anderson localization.