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arXiv 1201.1444astro-ph.COphysics.data-an
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关于N点关联函数描述非线性宇宙学场的不充分性：明确的例子和与模拟的联系

On the inadequacy of N-point correlation functions to describe nonlinear cosmological fields: explicit examples and connection to simulations

Julien Carron, Mark C. Neyrinck

备注：
10 pages, 3 figures, matches version accepted for publication by ApJ. Some editing in the conclusion and minor changes w.r.t. v1
发表信息：
ApJ, 750, 28 (2012)
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摘要：

出于最近的结果对数正态统计表明，时刻层次的对数正态变量完全无法捕捉其信息内容的大方差制度，我们在这项工作中讨论的不足层次的关联函数来描述一个相关的对数正态场，它提供了一个大致准确的描述非线性宇宙物质密度场。我们提出了家庭的字段具有相同的层次的关联函数比对数正态字段在所有订单。这明确地表明了一个很少研究的事实，即关联函数层次结构从来没有提供一个完整的描述对数正态场，它无法捕捉信息的非线性制度，其中其他简单的可观的是完全不受约束的。我们讨论了为什么微扰，Edgewise的方法来统计的非线性制度，常见的宇宙学，永远不能重现或预测的效果，以及为什么它是通用的尾场，暗示在故障的扰动理论的基础上的字段波动。我们做了一个粗略的，但成功的定量连接到N体模拟结果，这表明，对数密度场的频谱携带更多的信息比进入非线性政权的领域的频谱。

英文摘要：

Motivated by recent results on lognormal statistics showing that the moment hierarchy of a lognormal variable completely fails at capturing its information content in the large variance regime, we discuss in this work the inadequacy of the hierarchy of correlation functions to describe a correlated lognormal field, which provides a roughly accurate description of the non-linear cosmological matter density field. We present families of fields having the same hierarchy of correlation functions than the lognormal field at all orders. This explicitly demonstrates the little studied though known fact that the correlation function hierarchy never provides a complete description of a lognormal field, and that it fails to capture information in the non-linear regime, where other simple observables are left totally unconstrained. We discuss why perturbative, Edgeworth-like approaches to statistics in the non-linear regime, common in cosmology, can never reproduce or predict that effect, and why it is however generic for tailed fields, hinting at a breakdown of the perturbation theory based on the field fluctuations. We make a rough but successful quantitative connection to N-body simulations results, that showed that the spectrum of the log-density field carries more information than the spectrum of the field entering the non-linear regime.

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