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We explore two widely used empirical models for the galaxy-halo connection, subhalo abundance matching (SHAM) and the halo occupation distribution (HOD) and compare their predictions with the hydrodynamical simulation IllustrisTNG (TNG) for a range of statistics that quantify the galaxy distribution at $n_{\rm gal}\approx1.3\times10^{-3}\,[{\rm Mpc}/h]^{-3}$.
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