DISORDER-INDUCED DELOCALIZATION ON TREE GRAPHS

Highlighting a mechanism for the emergence of absolutely continuous spectrum through fluctuation-enabled resonance, we resolve an existing question concerning the mobility edge for Schrodinger operators with random (unbounded) potential on regular tree graphs. We find that the disorder driven resonance mechanism causes the somewhat surprising appearance of absolutely continuous spectrum well beyond the energy band of the operator's hopping term. For weak disorder this includes a Lifshits tail regime of very low density of states.