Cross-correlations between data sets are used in many different contexts in cosmological analyses. Recently, k-nearest neighbour cumulative distribution functions (kNN-CDF) were shown to be sensitive probes of cosmological (auto) clustering. In this paper, we extend the framework of NN measurements to describe joint distributions of, and correlations between, two data sets. We describe the measurement of joint kNN-CDFs, and show that these measurements are sensitive to all possible connected N-point functions that can be defined in terms of the two data sets. We describe how the cross-correlations can be isolated by combining measurements of the joint kNN-CDFs and those measured from individual data sets. We demonstrate the application of these measurements in the context of Gaussian density fields, as well as for fully non-linear cosmological data sets. Using a Fisher analysis, we show that measurements of the halo-matter cross-correlations, as measured through NN measurements are more sensitive to the underlying cosmological parameters, compared to traditional two-point cross-correlation measurements over the same range of scales. Finally, we demonstrate how the NN cross-correlations can robustly detect cross-correlations between sparse samples – the same regime where the two-point cross-correlation measurements are dominated by noise.

中文翻译：

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宇宙学互相关和最近邻分布

数据集之间的互相关用于宇宙学分析的许多不同环境中。最近，k-最近邻累积分布函数（kNN-CDF）被证明是宇宙学（自动）聚类的敏感探针。在本文中，我们扩展了 NN 测量的框架，以描述两个数据集的联合分布和相关性。我们描述了联合 kNN-CDF 的测量，并表明这些测量对可以根据两个数据集定义的所有可能的连接 N 点函数敏感。我们描述了如何通过结合对联合 kNN-CDF 的测量和从单个数据集测量的测量来隔离互相关。我们展示了这些测量在高斯密度场背景下的应用，以及完全非线性的宇宙学数据集。使用 Fisher 分析，我们表明，与相同尺度范围内的传统两点互相关测量相比，通过 NN 测量测量的晕物质互相关测量对潜在的宇宙学参数更敏感。最后，我们展示了 NN 互相关如何能够稳健地检测稀疏样本之间的互相关——这与两点互相关测量以噪声为主的情况相同。