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We present the first comprehensive halo occupation distribution (HOD) analysis of the Dark Energy Spectroscopic Instrument (DESI) One-Percent Survey luminous red galaxy (LRG) and Quasi Stellar Object (QSO) samples. We constrain the HOD of each sample and test possible HOD extensions by fitting the redshift-space galaxy 2-point correlation functions in 0.15 < r < 32 h−1 Mpc in a set of fiducial redshift bins. We use AbacusSummit cubic boxes at Planck 2018 cosmology as model templates and forward model galaxy clustering with the AbacusHOD package. We achieve good fits with a standard HOD model with velocity bias, and we find no evidence for galaxy assembly bias or satellite profile modulation at the current level of statistical uncertainty. For LRGs in 0.4 < z < 0.6, we infer a satellite fraction of $f_\mathrm{sat} = 11\pm 1~{y{\ \mathrm{per\,cent}}}$, a mean halo mass of $\log _{10}\overline{M}_h/M_\odot =13.40^{+0.02}_{-0.02}$, and a linear bias of $b_\mathrm{lin} = 1.93_{-0.04}^{+0.06}$. For LRGs in 0.6 < z < 0.8, we find $f_\mathrm{sat}=14\pm 1~{{\ \mathrm{per\,cent}}}$, $\log _{10}\overline{M}_h/M_\odot =13.24^{+0.02}_{-0.02}$, and $b_\mathrm{lin}=2.08_{-0.03}^{+0.03}$. For QSOs, we infer $f_\mathrm{sat}=3^{+8}_{-2}\mathrm{per\,cent}$, $\log _{10}\overline{M}_h/M_\odot = 12.65^{+0.09}_{-0.04}$, and $b_\mathrm{lin} = 2.63_{-0.26}^{+0.37}$ in redshift range 0.8 < z < 2.1. Using these fits, we generate a large suite of high fidelity galaxy mocks, forming the basis of systematic tests for DESI Y1 cosmological analyses. We also study the redshift-evolution of the DESI LRG sample from z = 0.4 up to z = 1.1, revealling significant and interesting trends in mean halo mass, linear bias, and satellite fraction.

We investigate using three-point statistics in constraining the galaxy–halo connection. We show that for some galaxy samples, the constraints on the halo occupation distribution parameters are dominated by the three-point function signal (over its two-point counterpart). We demonstrate this on mock catalogues corresponding to the Luminous red galaxies (LRGs), Emission-line galaxies (ELGs), and quasars (QSOs) targeted by the Dark Energy Spectroscopic Instrument (DESI) Survey. The projected three-point function for triangle sides less up to 20 h−1 Mpc measured from a cubic Gpc of data can constrain the characteristic minimum mass of the LRGs with a preci sion of 0.46 per cent. For comparison, similar constraints from the projected two-point function are 1.55 per cent. The improvements for the ELGs and QSOs targets are more modest. In the case of the QSOs, it is caused by the high shot-noise of the sample, and in the case of the ELGs, it is caused by the range of halo masses of the host haloes. The most time-consuming part of our pipeline is the measurement of the three-point functions. We adopt a tabulation method, proposed in earlier works for the two-point function, to significantly reduce the required compute time for the three-point analysis.