  We present the study of ten random realizations of a density field
characterized by a cosmological power spectrum P(k) at redshift z=50. The
reliability of such initial conditions for n-body simulations are tested with
respect to their correlation properties. The power spectrum P(k), and the mass
variance sigmaM(r) do not show detectable deviations from the desired behavior
in the intermediate range of scales between the mean interparticle distance and
the simulation volume. The estimator for xi(r) is too noisy to detect any
reliable signal at the initial redshift z=50. The particle distributions are
then evolved forward until z=0. This allows us to explore the cosmic variance
stemming from the random nature of the initial conditions. With cosmic variance
we mean the fact that a simulation represents a single realization of the
stochastic initial conditions whereas the real Universe contains many
realizations of regions of the size of the box; this problem affects most
importantly the scales at about the fundamental mode. We study morphological
descriptors of the matter distribution such as the genus, as well as the
internal properties of the largest object(s) forming in the box. We find that
the scatter is at least comparable to the scatter in the fundamental mode.
