Generalised Cumulant Correlators and Hierarchical Clustering
Generalised Cumulant Correlators and Hierarchical Clustering
复制标题
广义累积量相关器和层次聚类
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
P. Coles
中科院分区：
文献类型：
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作者：
D. Munshi;A. Melott;P. Coles
累积量涨落因子C_{pq}$是推广了更为人所知的S_p$参数的统计量，前者由密度涨落的两点概率分布函数得到，而后者只描述一点分布。如果星系成团是从高斯初始涨落发展起来的，并且采用小角近似，那么标准的微扰方法对于投影成团数据（如APM巡天）提出了一种特殊的$C_{pq}$等级关系。我们建立了有用的两点累积量描述层次聚类比较这种计算对现有的测量项目目录，发现非常好的协议。我们扩展的想法，累积量的多点{EM广义}累积量的消除器（相关的高阶相关函数）。我们扩展了之前在高度非线性区域的研究，以根据分层缩放模型的潜在“树振幅”来表达广义累积量相关器。这样的考虑导致一种技术，用于确定这些层次的振幅，以任意顺序，从星系目录和数值模拟。这些振幅的知识产生了重要的线索引力集群现象。例如，我们表明，三点累积量相关器可以用来分离的树振幅高达六阶。我们还结合联合收割机的Bernardeau和Schaeffer（1992）的特定的层次{emanalog}与扩展和超扩展的微扰理论来推断高度非线性区域中的树振幅值。
The cumulant correlators, $C_{pq}$, are statistical quantities that generalise the better-known $S_p$ parameters; the former are obtained from the two-point probability distribution function of the density fluctuations while the latter describe only the one-point distribution. If galaxy clustering develops from Gaussian initial fluctuations and a small-angle approximation is adopted, standard perturbative methods suggest a particular hierarchical relationship of the $C_{pq}$ for projected clustering data, such as the APM survey. We establish the usefulness of the two-point cumulants for describing hierarchical clustering by comparing such calculations against available measurements from projected catalogs, finding very good agreement. We extend the idea of cumulant correlators to multi-point {em generalised} cumulant correlators (related to the higher-order correlation functions). We extend previous studies in the highly nonlinear regime to express the generalised cumulant correlators in terms of the underlying ``tree amplitudes' of hierarchical scaling models. Such considerations lead to a technique for determining these hierarchical amplitudes, to arbitrary order, from galaxy catalogs and numerical simulations. Knowledge of these amplitudes yields important clues about the phenomenology of gravitational clustering. For instance, we show that three-point cumulant correlator can be used to separate the tree amplitudes up to sixth order. We also combine the particular hierarchical {em ansatz} of Bernardeau & Schaeffer (1992) with extended and hyperextended perturbation theory to infer values of the tree amplitudes in the highly nonlinear regime.