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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.

We present measurements of the redshift-dependent clustering of a DESI-like luminous red galaxy (LRG) sample selected from the Legacy Survey imaging data set, and use the halo occupation distribution (HOD) framework to fit the clustering signal. The photometric LRG sample in this study contains 2.7 million objects over the redshift range of 0.4 < z < 0.9 over 5655 deg2. We have developed new photometric redshift (photo-z) estimates using the Legacy Survey DECam and WISE photometry, with σNMAD = 0.02 precision for LRGs. We compute the projected correlation function using new methods that maximize signal-to-noise ratio while incorporating redshift uncertainties. We present a novel algorithm for dividing irregular survey geometries into equal-area patches for jackknife resampling. For a five-parameter HOD model fit using the MultiDark halo catalogue, we find that there is little evolution in HOD parameters except at the highest redshifts. The inferred large-scale structure bias is largely consistent with constant clustering amplitude over time. In an appendix, we explore limitations of Markov chain Monte Carlo fitting using stochastic likelihood estimates resulting from applying HOD methods to N-body catalogues, and present a new technique for finding best-fitting parameters in this situation. Accompanying this paper, we have released the Photometric Redshifts for the Legacy Surveys catalogue of photo-z's obtained by applying the methods used in this work to the full Legacy Survey Data Release 8 data set. This catalogue provides accurate photometric redshifts for objects with z < 21 over more than 16 000 deg2 of sky.