  In this work we study the properties of the mass density field in the
non-Gaussian world models simulated by Grossi et al. 2007. In particular we
focus on the one-point density probability distribution function of the mass
density field in non-Gausian models with quadratic non-linearities quantified
by the usual parameter f_NL. We find that the imprints of primordial
non-Gaussianity are well preserved in the negative tail of the probability
function during the evolution of the density perturbation. The effect is
already noticeable at redshifts as large as 4 and can be detected out to the
present epoch. At z=0 we find that the fraction of the volume occupied by
regions with underdensity delta < -0.9, typical of voids, is about 1.3 per cent
in the Gaussian case and increases to ~2.2 per cent if f_NL=-1000 while
decreases to ~0.5 per cent if f_NL=+1000. This result suggests that void-based
statistics may provide a powerful method to detect non-Gaussianity even at low
redshifts which is complementary to the measurements of the higher-order
moments of the probability distribution function like the skewness or the
kurtosis for which deviations from the Gaussian case are detected at the 25-50
per cent level.
