HectoMAP and Horizon Run 4: Dense Structures and Voids in the Real and
  Simulated Universe
  HectoMAP is a dense redshift survey of red galaxies covering a 53 $deg^{2}$
strip of the northern sky. HectoMAP is 97\% complete for galaxies with
$r<20.5$, $(g-r)>1.0$, and $(r-i)>0.5$. The survey enables tests of the
physical properties of large-scale structure at intermediate redshift against
cosmological models. We use the Horizon Run 4, one of the densest and largest
cosmological simulations based on the standard $\Lambda$ Cold Dark Matter
($\Lambda$CDM) model, to compare the physical properties of observed
large-scale structures with simulated ones in a volume-limited sample covering
8$\times10^6$ $h^{-3}$ Mpc$^3$ in the redshift range $0.22<z<0.44$. We apply
the same criteria to the observations and simulations to identify over- and
under-dense large-scale features of the galaxy distribution. The richness and
size distributions of observed over-dense structures agree well with the
simulated ones. Observations and simulations also agree for the volume and size
distributions of under-dense structures, voids. The properties of the largest
over-dense structure and the largest void in HectoMAP are well within the
distributions for the largest structures drawn from 300 Horizon Run 4 mock
surveys. Overall the size, richness and volume distributions of observed
large-scale structures in the redshift range $0.22<z<0.44$ are remarkably
consistent with predictions of the standard $\Lambda$CDM model.
