effectively have the same mass function as the overall sample. We also tested using binnings of 0.05 and 0.2 dex in halo mass finding no difference in our main results.

The HOD and the correlation function {#Sec:HOD_CF}
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To study the impact of assembly bias on galaxies we measure the halo occupation functions and the correlation functions for the various halo and galaxy samples.

The HOD formalism describes the “bias” relation between galaxies and mass at the level of individual haloes allowing us to characterize the galaxy-halo connection. The key ingredient is the halo occupation function, $\langle N(M_h) \rangle$, which represents, for a given galaxy sample, the average number of galaxies per halo as a function of halo mass (loosely referred to here also as the HOD). The commonly assumed shape for the halo occupation function is motivated by predictions of physical models such as SAMs and hydrodynamic simulations [@Berlind:2003; @Zheng:2005]. When inferring the HOD it is often useful to consider separately the contribution from central galaxies and that of the additional satellite galaxies populating the halo [@Kravtsov:2004; @Zheng:2005]. For stellar mass (or luminosity) threshold galaxy samples, the expected form of the central galaxies occupation function is a smoothed step 