  We study the structure and substructure of halos obtained in N-body
simulations for a Lambda Cold Dark Matter (LCDM) cosmology with non-Gaussian
initial conditions (NGICs). The initial statistics are lognormal in the
gravitational potential field with positive (LNp) and negative (LNn) skewness;
the sign of the skewness is conserved by the density field, and the power
spectrum is the same for all the simulations. Our aim is not to test a given
non-Gaussian statistics, but to explore the generic effect of positive- and
negative-skew statistics on halo properties. From our low-resolution
simulations, we find that LNp (LNn) halos are systematically more (less)
concentrated than their Gaussian counterparts. This result is confirmed by our
Milky Way- and cluster-sized halos resimulated with high-resolution. In
addition, they show inner density profiles that depend on the statistics: the
innermost slopes of LNp (LNn) halos are steeper (shallower) than those obtained
from the corresponding Gaussian halos. A subhalo population embedded in LNp
halos is more susceptible to destruction than its counterpart inside Gaussian
halos. On the other hand, subhalos in LNn halos tend to survive longer than
subhalos in Gaussian halos. The spin parameter probability distribution of LNp
(LNn) halos is skewed to smaller (larger) values with respect to the Gaussian
case. Our results show how the statistics of the primordial density field can
influence some halo properties, opening this the possibility to constrain,
although indirectly, the primordial statistics at small scale.
