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Weakly non-Gaussian formula for the Minkowski functionals in general dimensions
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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.
Forward citations
Cited by 2 Pith papers
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Non-Gaussian Expansion of Minkowski Tensors in Redshift Space
A first derivation of the non-Gaussian, redshift-space ensemble averages of two rank-2 Minkowski tensors, with percent-level agreement against Quijote simulations for smoothing scales above 20 Mpc/h.
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On the statistical nature of Betti numbers and Euler characteristic of smooth random fields
Betti numbers, Euler characteristic and their sum for excursion sets are expressed in terms of Binomial coefficients of a topological basis, predicting Gaussian statistics except at high thresholds.
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