  We prove that in dimension one the non-real eigenvalues of the non-Hermitian
Anderson (NHA) model with a selfaveraging potential are regularly spaced. The
class of selfaveraging potentials which we introduce in this paper is very wide
and in particular includes stationary potentials (with probability one) as well
as all quasi-periodic potentials. It should be emphasized that our approach
here is much simpler than the one we used before. It allows us a) to
investigate the above mentioned spacings, b) to establish certain properties of
the integrated density of states of the Hermitian Anderson models with
selfaveraging potentials, and c) to obtain (as a by-product) much simpler
proofs of our previous results concerned with non-real eigenvalues of the NHA
model.
