Starting from first principles, we derive the fundamental equations that relate the $n$-point correlation functions in real and redshift space. Our result generalises the so-called `streaming model' to higher-order statistics: the full $n$-point correlation in redshift-space is obtained as an integral of its real-space counterpart times the joint probability density of $n-1$ relative line-of-sight peculiar velocities. Equations for the connected $n$-point correlation functions are obtained by recursively applying the generalised streaming model for decreasing $n$. Our results are exact within the distant-observer approximation and completely independent of the nature of the tracers for which the correlations are evaluated. Focusing on 3-point statistics, we use an $N$-body simulation to study the joint probability density function of the relative line-of-sight velocities of pairs of particles in a triplet. On large scales, we find that this distribution is approximately Gaussian and that its moments can be accurately computed with standard perturbation theory. We use this information to formulate a phenomenological 3-point Gaussian streaming model. A practical implementation is obtained by using perturbation theory at leading order to approximate several statistics in real space. In spite of this simplification, the resulting predictions for the matter 3-point correlation function in redshift space are in rather good agreement with measurements performed in the simulation. We discuss the limitations of the simplified model and suggest a number of possible improvements. Our results find direct applications in the analysis of galaxy clustering but also set the basis for studying 3-point statistics with future peculiar-velocity surveys and experiments based on the kinetic Sunyaev-Zel'dovich effect.

中文翻译：

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n 点流模型：速度如何塑造红移空间中的相关函数

从第一性原理出发，我们推导出了在实空间和红移空间中关联 $n$ 点相关函数的基本方程。我们的结果将所谓的“流模型”推广到更高阶的统计数据：红移空间中完整的 $n$ 点相关性是作为其真实空间对应物乘以 $n-1 的联合概率密度的积分获得的$ 相对视距特殊速度。连接的$n$点相关函数的方程是通过递归地应用广义流模型来减少$n$而获得的。我们的结果在远距离观察者近似范围内是准确的，并且完全独立于评估相关性的示踪剂的性质。专注于三分统计，我们使用 $N$-body 模拟来研究三元组中粒子对的相对视线速度的联合概率密度函数。在大尺度上，我们发现该分布近似为高斯分布，并且可以使用标准微扰理论准确计算其矩。我们使用此信息来制定现象学 3 点高斯流模型。一个实际的实现是通过使用微扰理论以领先的顺序来逼近现实空间中的几个统计量。尽管进行了这种简化，但红移空间中物质 3 点相关函数的结果预测与模拟中执行的测量结果非常一致。我们讨论了简化模型的局限性，并提出了一些可能的改进建议。