The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to a large number of analyses of geometrical patterns, including various types of cosmic fields, morphological image processing, etc. In some cases, including cosmological applications in particular, small deviations from Gaussianity of distribution have a fundamental importance. Analytic formulas of expectation values of Minkowski functionals with small non-Gaussianity have been derived in limited cases so far. We generalize the previous work 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.
This talk is based on a paper in preparation with Satoshi Kuriki (ISM).