AI 中文总结
研究暗物质晕高阶构型空间聚类信息，通过GPU加速N点测量构建Fisher预测，将统计量视为阶梯，发现3PCF提供大部分高阶信息，连通4PCF进一步增加，该阶梯为高阶信息提供独立互补途径。
AI 中文摘要
两点相关函数完全描述高斯随机场，但非线性引力增长、晕偏置和红移空间畸变使晚期晕场呈强非高斯性，将大量宇宙学信息转移到高阶相关性中。我们在z = 0且固定数密度下，对Quijote暗物质晕的构型空间两点、三点和连通四点相关函数的信息含量进行量化。通过约38000次GPU加速的N点测量，构建了实空间和红移空间中针对{\Omega_m, \Omega_b, h, n_s, \sigma_8, M_\nu}的Fisher预测。将统计量视为阶梯（2PCF→+3PCF→+\zeta^{(4)}_{\mathrm{conn}}），报告了每一步获得的信息。3PCF提供了大部分可获取的高阶信息，连通4PCF进一步增加了约1.4 - 1.5倍。这种阶梯式增量对导数样本噪声和压缩正则化具有稳定性，绝对约束受有限模拟样本限制。我们用树级微扰理论模型验证了测量的3PCF，恢复了与2PCF一致的线性偏置。构型空间阶梯为傅里叶空间多谱探测的高阶信息提供了独立且互补的途径。
英文摘要
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 ${\sim}38{,}000$ GPU-accelerated $N$-point measurements. Treating the statistics as a ladder, $\mathrm{2PCF} \rightarrow +\mathrm{3PCF} \rightarrow +ζ^{(4)}_{\mathrm{conn}}$, 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 $\ge40\,h^{-1}{\rm Mpc}$, it still improves $M_ν$ by $3.9\times$. The connected 4PCF adds a further $\sim1.2$--$1.5\times$, an increment insensitive to whether the quadrupole is included in the baseline but traceable to small-scale configurations with sides $\lesssim30\,h^{-1}{\rm Mpc}$. 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.
Comments37 pages, 8 figures. Accepted in JCAP
