论文标题
最近的邻居分布：宇宙集群的新统计措施
Nearest Neighbor distributions: new statistical measures for cosmological clustering
论文作者
论文摘要
超出两点相关函数以外的摘要统计数据来分析在小尺度上的非高斯聚类是宇宙学研究领域。在本文中，我们探讨了一组新的摘要统计信息 - $ k $ - 最初的邻居累积分发功能（$ k {\ rm nn} $ - $ - $ {\ rm cdf} $）。这是从一组填充体积填充的，泊松分布的随机点到$ k $ neart的数据点的经验累积分布函数，并且对数据中的所有连接的$ n $ - 点相关性很敏感。 $ k {\ rm nn} $ - $ {\ rm cdf} $可用于测量单元格中的计数，空隙概率分布和较高的$ n $ - 点相关功能，所有这些都使用相同的形式主义利用与空间树数据结构的快速搜索相同的形式主义。我们演示了如何从各种数据集（包括离散点和连续字段的概括）中有效地计算出来。与两点相关函数相比，我们使用来自$ n $ body仿真的大型套件的数据来探讨该新统计数据对各种宇宙学参数的敏感性，同时使用相同的量表。我们证明，使用$ k {\ rm nn} $ - $ {\ rm cdf} $，将宇宙学参数的约束提高了$ 2 $的约束，将$ 2 $超过$ 2 $，将其应用于缩放范围内的暗物质范围$ 10H^{ - 1} { - 1} { - 1} {\ rm mpc} $ 40H和$ 40H MPC} $。我们还表明，当在相同的尺度上应用于在固定数量密度的模拟中，无论是在真实空间和红移空间中，相对改善都会更大。由于$ k {\ rm nn} $ - $ {\ rm cdf} $对数据中的所有高阶连接相关功能都很敏感，因此随着传统的两点分析的增长预计会增长，因为宇宙学数据的分析中包括逐渐较小的量表。
The use of summary statistics beyond the two-point correlation function to analyze the non-Gaussian clustering on small scales is an active field of research in cosmology. In this paper, we explore a set of new summary statistics -- the $k$-Nearest Neighbor Cumulative Distribution Functions ($k{\rm NN}$-${\rm CDF}$). This is the empirical cumulative distribution function of distances from a set of volume-filling, Poisson distributed random points to the $k$-nearest data points, and is sensitive to all connected $N$-point correlations in the data. The $k{\rm NN}$-${\rm CDF}$ can be used to measure counts in cell, void probability distributions and higher $N$-point correlation functions, all using the same formalism exploiting fast searches with spatial tree data structures. We demonstrate how it can be computed efficiently from various data sets - both discrete points, and the generalization for continuous fields. We use data from a large suite of $N$-body simulations to explore the sensitivity of this new statistic to various cosmological parameters, compared to the two-point correlation function, while using the same range of scales. We demonstrate that the use of $k{\rm NN}$-${\rm CDF}$ improves the constraints on the cosmological parameters by more than a factor of $2$ when applied to the clustering of dark matter in the range of scales between $10h^{-1}{\rm Mpc}$ and $40h^{-1}{\rm Mpc}$. We also show that relative improvement is even greater when applied on the same scales to the clustering of halos in the simulations at a fixed number density, both in real space, as well as in redshift space. Since the $k{\rm NN}$-${\rm CDF}$ are sensitive to all higher order connected correlation functions in the data, the gains over traditional two-point analyses are expected to grow as progressively smaller scales are included in the analysis of cosmological data.
