Spatial correlations of extended cosmological structures
  Studies of large-scale structures in the Universe, such as superstructures or
cosmic voids, have been widely used to characterize the properties of the
cosmic web through statistical analyses. On the other hand, the 2-point
correlation function of large-scale tracers such as galaxies or halos provides
a reliable statistical measure. However, this function applies to the spatial
distribution of point-like objects, and therefore it is not appropriate for
extended large structures which strongly depart from spherical symmetry. Here
we present an analysis based on the standard correlation function formalism
that can be applied to extended objects exhibiting arbitrary shapes. Following
this approach, we compute the probability excess $\Xi$ of having spheres
sharing parts of cosmic structures with respect to a realization corresponding
to a distribution of the same structures in random positions. For this aim, we
identify superstructures defined as Future Virialized Structures (FVSs) in
semi-anaytic galaxies on the MPDL2 MultiDark simulation. We have also
identified cosmic voids to provide a joint study of their relative distribution
with respect to the superstructures. Our analysis suggests that $\Xi$ provides
useful characterizations of the large scale distribution, as suggested from an
analysis of sub-sets of the simulation. Even when superstructure properties may
exhibit negligible variations across the sub-sets, $\Xi$ has the sensitivity to
statistically distinguish sub-boxes that departs from the mean at larger
scales. Thus, our methods can be applied in analysis of future surveys to
provide characterizations of large-scale structure suitable to distinguish
different theoretical scenarios.
