  Counts-in-cells are measured in the $\tau$CDM Virgo Hubble Volume simulation.
This large N-body experiment has 10^9 particles in a cubic box of size 2000
h^{-1} Mpc. The unprecedented combination of size and resolution allows for the
first time a realistic numerical analysis of the cosmic errors and cosmic
correlations of statistics related to counts-in-cells measurements, such as the
probability distribution function P_N itself, its factorial moments F_k and the
related cumulants $\xiav$ and S_N's. These statistics are extracted from the
whole simulation cube, as well as from 4096 sub-cubes of size 125 h^{-1}Mpc,
each representing a virtual random realization of the local universe. The
measurements and their scatter over the sub-volumes are compared to the
theoretical predictions of Colombi, Bouchet & Schaeffer (1995) for P_0, and of
Szapudi & Colombi (1996, SC) and Szapudi, Colombi & Bernardeau (1999a, SCB) for
the factorial moments and the cumulants. The general behavior of experimental
variance and cross-correlations as functions of scale and order is well
described by theoretical predictions, with a few percent accuracy in the weakly
non-linear regime for the cosmic error on factorial moments. (... more in paper
>...)
