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We prove that certain natural random variables associated with the localeigenvalue statistics for generalized lattice Anderson models constructed withfinite-rank perturbations are compound Poisson distributed. This distributionis characterized by the fact that the Levy measure is supported on at most afinite set determined by the rank. The proof relies on a Minami-type estimatefor finite-rank perturbations. For Anderson-type continuum models on $\R^d$, weprove a similar result for certain natural random variables associated with thelocal eigenvalue statistics. We prove that the compound Poisson distributionassociated with these random variables has a Levy measure whose support is atmost the set of positive integers.

Eigenvalue statistics for random Schrodinger operators with non rank one perturbations