EXPONENTIAL DECAY OF GREEN-FUNCTIONS FOR A CLASS OF LONG-RANGE HAMILTONIANS

We consider a class of long range Hamiltonians with diagonal disorder on l2 (Z). For any ergodic potential V with non-empty essential range, we prove the exponential decay of the Green's functions for energies in the essential range. If V is independent identically distributed, we obtain the exponential decay of the Green's functions for all coupling constant lambda > 0. Moreover the Hamiltonian has only pure point spectrum.