Abstract
An exact variational principle involving the density-of-eigenstates function is derived. This variational principle differs from previously published conjectures, and has been applied to two different types of band-tailing problems in order to demonstrate its usefulness. A closely related variational ansatz concerning the complex self-energy of a random medium is then formulated, and is shown, under the appropriate circumstances, to lead to the CPA approximation as well as to cluster generalizations of this approximation. It is shown that such cluster generalizations can accurately reproduce some computer-generated density of states.