We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of Luminous Red Galaxies (LRG) data collected during the initial two months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel'dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, nontrivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable datasets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.

翻译：我们针对暗能量光谱巡天仪器（DESI，第四代地面设施）前两个月运行期间收集的发光红星系（LRG）数据所对应的模拟星表，系统验证了两点相关函数（2PCF）的半解析半经验协方差矩阵。研究采用多条有效Zel'dovich（EZ）模拟星系星表，在施加相应数据截切后运行完整分析流程，并将结果与样本协方差进行对比以评估其精度及涨落特性。我们提出了针对经标准重构算法处理的星表所建立形式框架的扩展方案。通过详细比较协方差矩阵的比较方法，重点阐释了样本方差导致的统计性质及其物理解读——特别是当外部协方差估计完美时，某些度量指标的期望值仍呈现非平凡特征。借助改进的模拟星表与验证技术，我们证实了理论预测与样本协方差之间的高度一致性。该方法使研究者无需构建大量具有匹配成团特性的模拟星系星表，仅需利用数据本身的2PCF测量值即可生成可比数据集的协方差矩阵。本文所用代码已公开发布于 https://github.com/oliverphilcox/RascalC。