Climbing the N-point Ladder Part I: Information in the Higher-Order Configuration-Space Clustering of Dark Matter Halos
Abstract
We quantify the information content of the configuration-space two-, three-, and connected four-point correlation functions of Quijote dark-matter haloes at z=0 and fixed number density. We build Fisher forecasts for {Ωm, Ωb, h, ns, σ8, Mν} in real and redshift space from ∼38,000 GPU-accelerated N-point measurements. Treating the statistics as a ladder, 2PCF → +3PCF → +ζ(4)conn, we report the information gained at each rung. The 3PCF supplies most of the accessible higher-order information: it tightens every parameter, most strongly σ8 and Mν, whose degeneracy it partially breaks, by factors of $1.6−−6.3$ over the redshift-space {ξ0,ξ2} baseline with per-parameter gains consistent with those of the Fourier-space halo bispectrum on the same simulations. The 3PCF gains persist under conservative, modelling-motivated scale cuts: restricted to the tree-level-validated regime with minimum triangle side ≥40 h−1Mpc, it still improves Mν by 3.9×. The connected 4PCF adds a further ∼1.2--1.5×, an increment insensitive to whether the quadrupole is included in the baseline but traceable to small-scale configurations with sides ≲30 h−1Mpc. This rung-to-rung increment is stable against derivative-sample noise and compression regularization, whereas the absolute constraints remain limited by the finite simulation ensembles and are reported as preliminary. The configuration-space ladder thus offers an independent and complementary route to the higher-order information probed by the Fourier-space poly-spectra.
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BibTeX
@misc{kim2026climbing,
title = {{Climbing the $N$-point Ladder Part I: Information in the Higher-Order Configuration-Space Clustering of Dark Matter Halos}},
author = {Sumi Kim and Cristiano G. Sabiu and Inkyu Park},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.09116},
eprint = {2607.09116},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.09116},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Climbing the N-point Ladder Part I: Information in the Higher-Order Configuration-Space Clustering of Dark Matter Halos
AU - Sumi Kim
AU - Cristiano G. Sabiu
AU - Inkyu Park
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2607.09116
UR - https://arxiv.org/abs/2607.09116
AB - We quantify the information content of the configuration-space two-, three-, and connected four-point correlation functions of Quijote dark-matter haloes at z=0 and fixed number density. We build Fisher forecasts for {Ω_m, Ω_b, h, n_s, σ_8, M_ν} in real and redshift space from ∼38,000 GPU-accelerated N-point measurements. Treating the statistics as a ladder, 2PCF → +3PCF → +ζ^(4)_conn, we report the information gained at each rung. The 3PCF supplies most of the accessible higher-order information: it tightens every parameter, most strongly σ_8 and M_ν, whose degeneracy it partially breaks, by factors of $1.6−−6.3$ over the redshift-space {ξ_0,ξ_2} baseline with per-parameter gains consistent with those of the Fourier-space halo bispectrum on the same simulations. The 3PCF gains persist under conservative, modelling-motivated scale cuts: restricted to the tree-level-validated regime with minimum triangle side ≥40 h^−1Mpc, it still improves M_ν by 3.9×. The connected 4PCF adds a further ∼1.2--1.5×, an increment insensitive to whether the quadrupole is included in the baseline but traceable to small-scale configurations with sides ≲30 h^−1Mpc. This rung-to-rung increment is stable against derivative-sample noise and compression regularization, whereas the absolute constraints remain limited by the finite simulation ensembles and are reported as preliminary. The configuration-space ladder thus offers an independent and complementary route to the higher-order information probed by the Fourier-space poly-spectra.
ER -