星系$N$ -点关联函数的解析高斯协方差矩阵
Analytic Gaussian Covariance Matrices for Galaxy $N$-Point Correlation Functions
摘要：
本文导出了高斯极限下星系$N$ -点关联函数的协方差矩阵.我们的结果是针对任意$N$给出的，并投影到Cahn & Slepian（2020）的各向同性基函数上，最近表明这有助于有效的NPCF估计。4PCF协方差的数值实现相比，从一组对数正态模拟，Quijote暗物质晕目录，和MultiDark-Patchy星系模拟的样本协方差，后者包括现实的调查几何。的分析形式主义给出了合理的预测的协方差估计模拟与一个盒子的几何形状。此外，拟合的有效体积和数密度最大化的Kullback-Leibler发散的基础上的可能性，部分补偿的非均匀窗口函数的影响。
英文摘要：
We derive analytic covariance matrices for the $N$-Point Correlation Functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary $N$ and projected onto the isotropic basis functions of Cahn & Slepian (2020), recently shown to facilitate efficient NPCF estimation. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a non-uniform window function.
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