Weakly non-Gaussian formula for the Minkowski functionals in general dimensions

Abstract

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.

14 pages

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Cited by in corpus (7)

• Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?
• Probing massive neutrinos with the Minkowski functionals of large-scale structure
• The shape distribution of superclusters in SDSS DR 12
• Topology of Reionisation times: concepts, measurements and comparisons to gaussian random field predictions
• Statistical properties of Galactic synchrotron temperature and polarization maps -- a multi-frequency comparison
• Numerical investigation of non-Gaussianities in the phase and modulus of density Fourier modes
• Asymptotic expansion of the expected Minkowski functional for isotropic central limit random fields