宇宙学互相关和最近邻分布
Cosmological cross-correlations and nearest neighbor distributions
摘要：
在宇宙学分析中，数据集之间的互相关被用于许多不同的背景。最近，最近邻累积分布函数（$k$ - ${\rm CDF}$）被证明是宇宙学（自动）聚类的敏感探针。在本文中，我们扩展了最近邻测量的框架来描述两个数据集之间的联合分布和相关性。我们描述的测量联合$k{\rm NN}$ - ${\rm CDF}$的，并表明，这些测量是敏感的所有可能的连接$N$ -点函数，可以定义在两个数据集。我们描述了如何可以通过结合测量的联合$k{\rm NN}$ - ${\rm CDF}$ s和那些从单独的数据集测量的互相关隔离。我们展示了这些测量的应用在高斯密度场的背景下，以及完全非线性宇宙学数据集。使用Fisher分析，我们表明，测量的晕物质的互相关，通过最近邻测量更敏感的基本宇宙学参数相比，传统的两点互相关测量在同一范围内的尺度。最后，我们演示了如何最近邻互相关可以鲁棒地检测稀疏样本之间的互相关-相同的制度，其中两点互相关测量是由噪声占主导地位。
英文摘要：
Cross-correlations between datasets are used in many different contexts in cosmological analyses. Recently, $k$-Nearest Neighbor Cumulative Distribution Functions ($k{\rm NN}$-${\rm CDF}$) were shown to be sensitive probes of cosmological (auto) clustering. In this paper, we extend the framework of nearest neighbor measurements to describe joint distributions of, and correlations between, two datasets. We describe the measurement of joint $k{\rm NN}$-${\rm CDF}$s, and show that these measurements are sensitive to all possible connected $N$-point functions that can be defined in terms of the two datasets. We describe how the cross-correlations can be isolated by combining measurements of the joint $k{\rm NN}$-${\rm CDF}$s and those measured from individual datasets. We demonstrate the application of these measurements in the context of Gaussian density fields, as well as for fully nonlinear cosmological datasets. Using a Fisher analysis, we show that measurements of the halo-matter cross-correlations, as measured through nearest neighbor 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 nearest neighbor cross-correlations can robustly detect cross correlations between sparse samples -- the same regime where the two-point cross-correlation measurements are dominated by noise.
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