Jaksic V., Molchanov S.
Localization for one dimensional long range random Hamiltonians
(213K, postscript)

ABSTRACT.  We study spectral properties of random Schrodinger operators 
$h_\omega = h_0 + v_\omega(n)$ on $l^2({\bf Z})$ whose free part 
$h_0$ is long range. We prove that the spectrum of $h_\omega$ 
is pure point for typical $\omega$ if the random variables $v_\omega(n)$ 
have sufficently long tails and if off-diagonal terms of $h_0$ decay as 
$\vert i-j \vert^{-\gamma}$ for some $\gamma >8$.