  We consider Schr\"odinger operator with random decaying potential on $\ell^2
({\bf Z}^d)$ and showed that, (i) IDS coincides with that of free Laplacian in
general cases, and (ii) the set of extremal eigenvalues, after rescaling,
converges to a inhomogeneous Poisson process, under certain condition on the
single-site distribution, and (iii) there are "border-line" cases, such that we
have Poisson statistics in the sense of (ii) above if the potential does not
decay, while we do not if the potential does decay.
