Related papers: Asymptotic expansion of the expected Minkowski fun…
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…
The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial…
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…
Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level $u$ chosen to control the tail probability or $p$-value of its maximum. This $p$-value is approximated by the…
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…
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…
We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
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…
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…
Spherical spin random fields are used to model the Cosmic Microwave Background polarization, the study of which is at the heart of modern Cosmology and will be the subject of the LITEBIRD mission, in the 2030s. Its scope is to collect datas…
The formalism to compute the geometrical and topological one-point statistics of mildly non-Gaussian 2D and 3D cosmological fields is developed. Leveraging the isotropy of the target statistics, the Gram-Charlier expansion is reformulated…
We give a systematic and thorough study of geometric notions and results connected to Minkowski's measure of symmetry and the extension of the well-known Minkowski functional to arbitrary, not necessarily symmetric convex bodies K on any…
We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which…
Rayleigh-L\'evy flights are simplified cosmological tools which capture certain essential statistical properties of the cosmic density field, including hierarchical structures in higher-order correlations, making them a valuable reference…
We present a novel method for computing the Minkowski Functionals from isodensity surfaces extracted directly from the Delaunay tessellation of a point distribution. This is an important step forward compared to the previous cosmological…
The expected Euler characteristic (EEC) curve of excursion sets of a Gaussian random field is used to approximate the distribution of its supremum for high thresholds. Viewed as a function of the excursion threshold, the EEC is expressed by…
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 apply the morphological descriptions of two-dimensional contour map, the so-called Minkowski functionals (the area fraction, circumference, and Euler characteristics), to the convergence field $\kappa(\bm{\theta})$ of the large-scale…
We present measurements of the Minkowski functionals extracted from the SDSS-III BOSS catalogs. After defining the Minkowski functionals, we describe how an unbiased reconstruction of these statistics can be obtained from a field with…