Exponential decay of Green's functions for a class of long range Hamiltonians

We consider a class of long range Hamiltonians with diagonal disorder onl² (Z). For anyergodic potentialV with non-empty essential range, we prove the exponential decay of the Green's functions for energies in the essential range. IfV is independent identically distributed, we obtain the exponential decay of the Green's functions for all coupling constant >0. Moreover the Hamiltonian has only pure point spectrum.