Experimental cosmic statistics - I. Variance

Counts-in-cells are measured in the τCDM 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 PN itself, its factorial moments Fk and the related cumulants ξ and SN’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 P0, 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