What do simulations predict for the galaxy stellar mass function and its
  evolution in different environments?
  We present a comparison between the observed galaxy stellar mass function and
the one predicted from the De Lucia & Blaizot (2007) semi-analytic model
applied to the Millennium Simulation, for cluster satellites and galaxies in
the field (meant as a wide portion of the sky, including all environments), in
the local universe (z~0.06) and at intermediate redshift (z~0.6), with the aim
to shed light on the processes which regulate the mass distribution in
different environments. While the mass functions in the field and in its finer
environments (groups, binary and single systems) are well matched in the local
universe down to the completeness limit of the observational sample, the model
over-predicts the number of low mass galaxies in the field at z~0.6 and in
clusters at both redshifts. Above M_*=10^10.25 M_sun, it reproduces the
observed similarity of the cluster and field mass functions, but not the
observed evolution. Our results point out two shortcomings of the model: an
incorrect treatment of cluster-specific environmental effects and an
over-efficient galaxy formation at early times (as already found by e.g.
Weinmann et al. 2012). Next, we consider only simulations. Using also the Guo
et al. (2011) model, we find that the high mass end of the mass functions
depends on halo mass: only very massive halos host massive galaxies, with the
result that their mass function is flatter. Above M_*=10^9.4 M_sun, simulations
show an evolution in the number of the most massive galaxies in all the
environments. Mass functions obtained from the two prescriptions are different,
however results are qualitatively similar, indicating that the adopted recipes
to model the evolution of central and satellite galaxies still have to be
better implemented in semi-analytic models.
