论文标题
Minkowski功能在一般维度中的弱非高斯公式
Weakly non-Gaussian formula for the Minkowski functionals in general dimensions
论文作者
论文摘要
Minkowski功能是量化各种随机场的形态的有用统计数据。它们已被应用于对几何模式的众多分析，包括各种类型的宇宙田，形态图像处理等。在某些情况下，包括宇宙学应用，与分布的高斯高斯的小偏差至关重要。迄今为止有限的情况下，已经得出了具有小非高斯性的Minkowski功能的期望值的分析公式。我们概括了这些先前的作品，以得出Minkowski功能的期望值的分析表达，在一般维度的一个空间中，直至非高斯性的二阶校正。派生公式具有足够的一般性，可应用于任何维度的统计均匀和各向同性空间中的任何随机场。
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.
