Localization for transversally periodic random potentials on binary trees

Abstract

We consider a random Schrodinger operator on the binary tree with a random poten- tial which is the sum of a random radially symmetric potential, Qr, and a random transversally periodic potential, Q t, with coupling constant . Using a new one-dimensional dynamical systems approach combined with Jensen's inequality in hyperbolic space (our key estimate) we obtain a fractional moment estimate proving localization for small and large . Together with a previous result we therefore obtain a model with two Anderson transitions, from localization to delocaliza- tion and back to localization, when increasing . As a by-product we also have a partially new proof of one-dimensional Anderson localization at any disorder.