Asymptotic expansion of the expected Minkowski functional for isotropic central limit random fields

Abstract The Minkowski functionals, including the Euler characteristic statistics, are standard tools for morphological analysis in cosmology. Motivated by cosmic research, we examine functional of excursion set an isotropic central limit random field, whose k -point correlation functions ( th-order cumulants) have same structure as that assumed research. Using 3- and 4-point functions, derive asymptotic expansions density, which is building block functional. resulting formula reveals types non-Gaussianity cannot be captured functionals. As example, consider chi-squared field confirm expansion accurately approximates true density.