2020/11/10 by Takahiko Matsubara, Satoshi Kuriki
Computer Science · Environmental Science · Health Professions · Mathematics · Physics and Astronomy · #Atmospheric and Environmental Gas Dynamics #Computer science #Distribution (mathematics) #Gaussian #Generality #Geochemistry and Geologic Mapping #Homogeneous #Isotropy #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Physics #Quantum mechanics #Radioactivity and Radon Measurements #Random field #Space (punctuation) #Statistical physics #Statistics #astro-ph.CO
paper · pdf · doi:10.1103/physrevd.104.103522
14 pages
arxiv created 2020/11/10 · openalex publication_date 2021/11/18 · arxiv updated 2021/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.