Cell Count Moments in the Halo Model
  We study cell count moments up to fifth order of the distributions of haloes,
of halo substructures as a proxy for galaxies, and of mass in the context of
the halo model and compare theoretical predictions to the results of numerical
simulations. On scales larger than the size of the largest cluster, we present
a simple point cluster model in which results depend only on cluster-cluster
correlations and on the distribution of the number of objects within a cluster,
or cluster occupancy. The point cluster model leads to expressions for moments
of galaxy counts in which the volume-averaged moments on large scales approach
those of the halo distribution and on smaller scales exhibit hierarchical
clustering with amplitudes $S_k$ determined by moments of the occupancy
distribution. In this limit, the halo model predictions are purely
combinatoric, and have no dependence on halo profile, concentration parameter,
or potential asphericity. The full halo model introduces only two additional
effects: on large scales, haloes of different mass have different clustering
strengths, introducing relative bias parameters; and on the smallest scales,
halo structure is resolved and details of the halo profile become important,
introducing shape-dependent form factors. Because of differences between
discrete and continuous statistics, the hierarchical amplitudes for galaxies
and for mass behave differently on small scales even if galaxy number is
exactly proportional to mass, a difference that is not necessarily well
described in terms of bias.
