Constraining galaxy-halo connection with high-order statistics

We investigate the usage of three-point statistics in constraining 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 catalogs corresponding to the luminous red galaxies (LRG), emission-line galaxies (ELG), and quasars (QSO) targeted by the Dark Energy Spectroscopic Instrument (DESI) Survey. The projected three-point function in the range of up to 20 h^-1 Mpc measured from a cubic Gpc of data can constrain the characteristic minimum mass of the LRGs with a precision of 0.46 percent. For comparison, similar constraints from the projected two-point function are 1.55 percent. The improvements for the ELG and QSO 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, this is caused by the range of halo masses of the host halos. 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 computing time required for the three-point analysis.