Related papers: Weakly non-Gaussian formula for the Minkowski func…
Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for…
Analytic formulas of Minkowski functionals in two-dimensional random fields are derived, including effects of second-order non-Gaussianity in the presence of both the bispectrum and trispectrum. The set of formulas provides a promising…
The second-order formula of Minkowski functionals in weakly non-Gaussian fields is compared with the numerical $N$-body simulations. Recently, weakly non-Gaussian formula of Minkowski functionals is extended to include the second-order…
Minkowski Functionals (MFs) are topological statistics that have become one of many standard tools used for investigating the statistical properties of cosmological random fields. They have found regular use in studies of departures from…
In the context of upcoming large-scale structure surveys such as Euclid, it is of prime importance to quantify the effect of peculiar velocities on geometric probes. Hence the formalism to compute in redshift space the geometrical and…
We present a new harmonic-domain approach for extracting morphological information, in the form of Minkowski Functionals (MFs), from weak lensing (WL) convergence maps. Using a perturbative expansion of the MFs, which is expected to be…
The Minkowski functionals are a mathematical tool to quantify morphological features of patterns. Some applications to the matter distribution in galaxy catalogues and N-body simulations are reviewed, with an emphasis on the effects of…
A Gaussian distribution of cosmic microwave background temperature fluctuations is a generic prediction of inflation. Upcoming high-resolution maps of the microwave background will allow detailed tests of Gaussianity down to small angular…
Minkowski functionals provide a novel tool to characterize the large-scale galaxy distribution in the Universe. Here we give a brief tutorial on the basic features of these morphological measures and indicate their practical application for…
The genus statistics of isodensity contours has become a well-established tool in cosmology. In this Letter we place the genus in the wider framework of a complete family of morphological descriptors. These are known as the Minkowski…
The Gaussian Kinematic Formula (GKF, see Adler and Taylor (2007,2011)) is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for…
The morphological properties of large scale structure of the Universe can be fully described by four Minkowski functionals (MFs), which provide important complementary information to other statistical observables such as the widely used…
In order to quantify higher-order correlations of the galaxy cluster distribution we use a complete family of additive measures which give scale-dependent morphological information. Minkowski functionals can be expressed analytically in…
In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowski functionals. These functionals appear as coefficients in the probability content of a tube…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…
Minkowski functionals have recently been introduced into cosmology as novel tools for studying the large-scale distribution of matter in the Universe. We present a brief overview of the method, including its mathematical foundations as well…
The Minkowski functionals, including the Euler characteristic statistics, are standard tools for morphological analysis in cosmology. Motivated by cosmic research, we examine the Minkowski functional of the excursion set for an isotropic…
In this paper, we show that Minkowski Functionals (MFs) of weak gravitational lensing (WL) convergence maps contain significant non-Gaussian, cosmology-dependent information. To do this, we use a large suite of cosmological ray-tracing…
We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of…
We suggest novel statistics for the CMB maps that are sensitive to non-Gaussian features. These statistics are natural generalizations of the geometrical and topological methods that have been already used in cosmology such as the…