properties).

The concentration of haloes with a small number of particles (fewer than 200 particles or $M_h < 10^{11.26} h^{-1} {\rm M_{ \odot}}$, ie. the red lines in Fig. \[Fig:CP\]) could be underestimated due to resolution effects [@Trenti:2010; @Paranjape:2017]. Most of the following analysis uses halo masses above this threshold and ranks samples in halo concentration at fixed mass, rather than using its actual value; we expect that our results should be unaffected by this possible source of systematics.

![image](Fig3a.pdf){width="47.00000%"} ![image](Fig3b.pdf){width="47.00000%"}

We now look into the CF of halo samples with different concentrations and formation times for a fixed number density after rank ordering the haloes in decreasing mass at $z=0$ and $z=3$ (Fig. \[Fig:CF\_Ev\]). We use a halo number density of $n = 0.00618 \, h^{3}\, {\rm Mpc}^{-3}$, which is comparable to the number density of central galaxies in the $n = 0.01 \, h^{3}\, {\rm Mpc}^{-3}$ galaxy sample (when selecting galaxies by their stellar mass). The equivalent halo mass (peak height) cut for these samples are $10^{11.75}\ h^{-1}M_{\odot}$ (0.76) for $z=0$ and $10^{11.24}\ h^{-1}M_{\odot}$ (2.01) for $z=3$. In each subplot of Fig. \[Fig:CF\_Ev\], the black line in the top panel denotes the auto CF of the full halo 