is very uncertain in this scheme, since they are expected to be very faint, and have therefore very little weight in the sum of the total luminosity, while they can contribute an important fraction of the mass. Another important point is that in principle the luminosity of the galaxies that were contained in the destroyed subhaloes should be added to the central galaxy luminosity, since under this scheme we are assuming that these are merging. In practice, though, the light in these destroyed subhaloes is going to be small in comparison with the BCG in this model, since the largest fraction of destroyed subhaloes occurs for less massive haloes where the BCG is dominant. For simplicity, we will here ignore this contribution.

Introducing scatter {#sect:scatter}
===================

The conditional luminosity function
-----------------------------------

In the context of the present paper, we need a more detailed model than the one described previously. Most importantly, it needs to include some kind of scatter in the mass-luminosity relation. Naturally, we expect that not all galaxies in hosts of the same mass will have the same luminosity. To capture this, we introduce a dispersion around the average relation describe above. We use the conditional luminosity function 