Jaksic V., Molchanov S.
Localization for One Dimensional Long 
Range Random Hamiltonians - revised and extended version. 
(740K, postscript)

ABSTRACT.  We study spectral properties of random Schr\"odinger 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 $\omega$ whenever the   
off-diagonal terms of $h_0$ decay as $\vert i -j\vert^{-\gamma}$ for 
some $\gamma >8$.