高斯随机场中的峰和谷：剪切本征值的新算法和偏移集理论
Peaks and dips in Gaussian random fields: a new algorithm for the shear eigenvalues, and the excursion set theory
摘要：
我们提出了一种新的算法来采样与高斯统计相关联的初始剪切场的约束特征值，称为“基于峰/谷偏移集”的算法，在对应于相关密度场的峰或谷的位置。计算过程是基于一个新的公式，该公式扩展了Doroshkevich的线性潮汐场的本征值的无条件分布，考虑到晕和空隙可能对应于密度场的最大值或最小值的事实。区分空间中的随机位置和特殊点（在这些点周围可能形成晕圈或空洞（峰/谷））的能力，在新公式中编码并在算法中反映，自然导致高斯随机场中峰和谷的偏移集模型的直接实现-该采样过程的关键优点之一。此外，它为宇宙网络的统计描述提供了新的见解。作为第一个物理应用程序，我们展示了如何在三轴模型的结构形成的剪切椭圆率和长轴性的标准分布修改的约束。特别是，我们提供了一个新的表达式的条件分布的形状参数给定的密度峰值约束，推广了以前的一些文献工作。该公式对于非球形暗物质晕形状的建模具有重要意义，与它们的初始形状分布有关。我们还测试和确认我们的理论预测的个别分布的特征值的极值约束，以及其他直接相关的条件概率。最后，我们指出了如何自然地融入标准的偏移集模型，可能解决其一些众所周知的问题，并进入椭球崩溃框架所提出的采样过程。（节略）
英文摘要：
We present a new algorithm to sample the constrained eigenvalues of the initial shear field associated with Gaussian statistics, called the `peak/dip excursion-set-based' algorithm, at positions which correspond to peaks or dips of the correlated density field. The computational procedure is based on a new formula which extends Doroshkevich's unconditional distribution for the eigenvalues of the linear tidal field, to account for the fact that halos and voids may correspond to maxima or minima of the density field. The ability to differentiate between random positions and special points in space around which halos or voids may form (peaks/dips), encoded in the new formula and reflected in the algorithm, naturally leads to a straightforward implementation of an excursion set model for peaks and dips in Gaussian random fields - one of the key advantages of this sampling procedure. In addition, it offers novel insights into the statistical description of the cosmic web. As a first physical application, we show how the standard distributions of shear ellipticity and prolateness in triaxial models of structure formation are modified by the constraint. In particular, we provide a new expression for the conditional distribution of shape parameters given the density peak constraint, which generalizes some previous literature work. The formula has important implications for the modeling of non-spherical dark matter halo shapes, in relation to their initial shape distribution. We also test and confirm our theoretical predictions for the individual distributions of eigenvalues subjected to the extremum constraint, along with other directly related conditional probabilities. Finally, we indicate how the proposed sampling procedure naturally integrates into the standard excursion set model, potentially solving some of its well-known problems, and into the ellipsoidal collapse framework. (abridged)
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