  As a supplement of our previous work, we consider the localized region of the
random Schroedinger operators on $l^2({\bf Z}^d)$ and study the point process
composed of their eigenvalues and corresponding localization centers. For the
Anderson model, we show that, this point process in the natural scaling limit
converges in distribution to the Poisson process on the product space of energy
and space. In other models with suitable Wegner-type bounds, we can at least
show that any limiting point processes are infinitely divisible.
