to the observed mass function $\Phi_{obs}(m)$ by @panter2007, we choose the same stellar mass range ($10^{8.5}-10^{11.85}~{\!\,{\rm M}_\odot}$) and the same binsize. The observed SMF was derived using spectra from the Sloan Digital Sky Survey Data Release 3 (SDSS DR3); see @panter2004 for a description of the method.

Furthermore it is possible to determine the stellar mass dependent clustering of galaxies. For this we compute projected galaxy CFs $w_{p,mod}(r_p,m_i)$ in several stellar mass bins which we choose to be the same as in the observed projected galaxy CFs of @li06. These were derived using a sample of galaxies from the SDSS DR2 with stellar masses estimated from spectra by @kauffmann03.

We first calculate the real space CF $\xi(r)$. In a simulation this can be done by simply counting pairs in distance bins: $$\label{corrfunc}
\xi(r_i) = \frac{dd(r_i)}{N_p(r_i)}-1$$ where $dd(r_i)$ is the number of pairs counted in a distance bin and $N_p(r_i) = 2 \pi N^2 r_i^2 \Delta r_i / L_{\rm box}^3$ where $N$ is the total number of galaxies in the box. The projected CF $w_p(r_p)$ can be derived by integrating the real space correlation function $\xi(r)$ along the line of sight: $$w_p(r_p) = 2 \int_{0}^{\infty} {\rm d}r_{||} \xi(\sqrt{r_{||}^2+r_p^2}) = 2 \int_{r_p}^{\infty} 