Weakly non-Gaussian formula for the Minkowski functionals in general dimensions
Weakly non-Gaussian formula for the Minkowski functionals in general dimensions
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DOI：
10.1103/physrevd.104.103522
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发表时间：
2020-11
影响因子：
5
通讯作者：
T. Matsubara;S. Kuriki
中科院分区：
文献类型：
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作者：
T. Matsubara;S. Kuriki
闵可夫斯基泛函是量化各种随机场形态的有用统计数据。它们已应用于多种几何图案分析，包括各种类型的宇宙场、形态图像处理等。在某些情况下，包括宇宙学应用，与分布高斯性的微小偏差至关重要。迄今为止，已经在有限的情况下导出了具有小非高斯性的闵可夫斯基泛函期望值的解析公式。我们对这些先前的工作进行了概括，导出了闵可夫斯基泛函期望值的解析表达式，直至一般维度空间中非高斯性的二阶校正。推导的公式具有足够的通用性，可以应用于任何维度的统计均匀且各向同性空间中具有弱非高斯性的任何随机场。
The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to numerous analyses of geometrical patterns, including various types of cosmic fields, morphological image processing, etc. In some cases, including cosmological applications, small deviations from the Gaussianity of the distribution are of fundamental importance. Analytic formulas for the expectation values of Minkowski functionals with small non-Gaussianity have been derived in limited cases to date. We generalize these previous works to derive an analytic expression for expectation values of Minkowski functionals up to second-order corrections of non-Gaussianity in a space of general dimensions. The derived formula has sufficient generality to be applied to any random fields with weak non-Gaussianity in a statistically homogeneous and isotropic space of any dimensions.