Kirsch W., Krishna M., Obermeit J.
Anderson Model with decaying randomness: Mobility Edge
(36K, LATeX 2e)

ABSTRACT.  \abstract{In this paper we consider the Anderson model with
decaying randomness $a_nq_{\omega}(n)$,  $a_n > 0, n \in
\ZZ^{\nu}$ and
$q_{\omega}(n)$, i.i.d random variables with an absolutely
continuous distribution $\mu$.  For a class of $\mu$ 
we show the following results on a set
$\omega$ of full measure.
(i) If $|a_n| \rightarrow 0$ as $|n| \rightarrow \infty$, then 
    $\sigma_c(H_{\omega}) \subseteq [-2\nu, 2\nu]$
(ii) $\sigma(H_{\omega}) = \RR$.
(iii) If $|a_n| \leq (|n|^{-1-\epsilon})$ for large $|n|$ and $\nu
\geq 3$, the mobility edges are the two points $\{-2\nu, 2\nu\}$.