... slope

The subtle differences in the cosmological parameters adopted in this work with respect to those in the Millennium simulation ( $\Omega_{\rm m}=0.25$, $\Omega_\Lambda=0.75$, h=0.73) are unlikely to have any significant impact on our results.

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... simulation

See http://www.g-vo.org/Millennium.

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... galaxies

In the R band, the characteristic luminosity of $z\sim 0$ early type galaxies L_* is M^*_R=-21.5 (Baldry et al. 2004).

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