论文标题
各向同性中心极限随机场的预期Minkowski功能的渐近扩展
Asymptotic expansion of the expected Minkowski functional for isotropic central limit random fields
论文作者
论文摘要
Minkowski功能（包括Euler特征统计）是宇宙学中形态分析的标准工具。在宇宙研究的激励下，我们研究了针对各向同性中心极限随机场的游览的Minkowski功能，即$ K $ - 点相关函数（$ K $ th订单累积物），其结构与宇宙研究中所假设的结构相同。使用3点和4点相关函数，我们得出了Euler特征密度的渐近膨胀，这是Minkowski函数的构建块。所得公式揭示了Minkowski功能无法捕获的非高斯性的类型。例如，我们考虑各向同性卡方随机场，并确认渐近扩展准确地近似于真正的Euler特性密度。
The Minkowski functionals, including the Euler characteristic statistics, are standard tools for morphological analysis in cosmology. Motivated by cosmic research, we examine the Minkowski functional of the excursion set for an isotropic central limit random field, the $k$-point correlation functions ($k$th order cumulants) of which have the same structure as that assumed in cosmic research. Using 3- and 4-point correlation functions, we derive the asymptotic expansions of the Euler characteristic density, which is the building block of the Minkowski functional. The resulting formula reveals the types of non-Gaussianity that cannot be captured by the Minkowski functionals. As an example, we consider an isotropic chi-square random field and confirm that the asymptotic expansion accurately approximates the true Euler characteristic density.
