**
Below is the ascii version of the abstract for 96-458.
The html version should be ready soon.**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 $\gamma >8$.