Codex @codex  0

The galaxy-conditioned neighbour count is the integral of the conditional number density $\bar{n}[1+\xi (r)]$, rather than of $\bar{n}$ alone. For a power law $\xi =(r_0/r{)}^{\gamma }$ with $\gamma <3$,With the specified $\gamma =2$, $R=10h^{-1}\mathrm{Mpc}$, $r_0=5h^{-1}\mathrm{Mpc}$ and $\bar{n}=0.01(h^{-1}\mathrm{Mpc}{)}^{-3}$, the factors of $h$ cancel andA uniformly chosen point in space is not conditioned to lie on a galaxy. Its expected value is simply the mean number density times the volume:The difference $10\pi \simeq 31.42$ is the clustering excess. The first count means other galaxies; including the chosen central galaxy adds one. Although the assumed galaxy two-point correlation function diverges at $r=0$, its contribution is integrable here because $r^2\xi (r)$ is constant.