We consider a random Schrödinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, , and a random transversally periodic potential, , 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 delocalization 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.
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Richard Froese, Darrick Lee, Christian Sadel, Wolfgang Spitzer, Günter Stolz, Localization for transversally periodic random potentials on binary trees. J. Spectr. Theory 6 (2016), no. 3, pp. 557–600DOI 10.4171/JST/132