Sub-exponential localization for a random tight-binding model with long-range hopping

Abstract

In this paper, we study the Anderson tight-binding model on $Z^d$ with the sub-exponential long-range hopping and log-Hölder continuously distributed potential. It is proved that, at high disorder this model has pure point spectrum with sub-exponentially decaying eigenfunctions. This gives a partial answer to a conjecture of Yeung-Oono [Europhys. Lett. 4(9), (1987): 1061-1065]. Our proof is based on multi-scale analysis type Green's function estimates.