Related papers: Voronoi chords in flat cosmology
We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our…
Cells of Voronoi diagrams in two dimensions are usually considered as having edges of zero width. However, this is not the case in several experimental situations in which the thickness of the edges of the cells is relatively large. In this…
Studies of large-scale structures in the Universe, such as superstructures or cosmic voids, have been widely used to characterize the properties of the cosmic web through statistical analyses. On the other hand, the 2-point correlation…
We apply the framework of Vlasov Perturbation Theory (VPT) to the two-loop matter power spectrum within $\Lambda$CDM cosmologies. The main difference to Standard Perturbation Theory (SPT) arises from taking the velocity dispersion tensor…
We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random…
Void number counts (VNC) indicates the number of low-density regions in the large-scale structure (LSS) of the Universe, and we propose to use it as an effective cosmological probe. By generating the galaxy mock catalog based on Jiutian…
The aim of this study is to distinguish genuine cosmic voids, found in a galaxy catalog by the void finder ZOBOV-VIDE, from under-dense regions in a Poisson distribution of objects. For this purpose, we perform two multivariate analyses…
CONTEXT: Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect…
Quantization of a probability distribution is the process of estimating a given probability by a discrete probability that assumes only a finite number of levels in its support. Centroidal Voronoi tessellations (CVT) are Voronoi…
A novel algorithm to detect coherent structures with sparse Lagrangian particle tracking data, using Voronoi tessellation and techniques from spectral graph theory, is tested. Neighbouring tracer particles are naturally identified through…
Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…
We have developed a novel method of determining 2D radial density profiles for astronomical systems of discrete objects using Voronoi tessellations. This Voronoi-based method was tested against the standard annulus-based method on 5…
Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate…
The intersections of beta-Voronoi, beta-prime-Voronoi and Gaussian-Voronoi tessellations in $\mathbb{R}^d$ with $\ell$-dimensional affine subspaces, $1\leq \ell\leq d-1$, are shown to be random tessellations of the same type but with…
In this paper, we develop the method of analyzing the velocity field of cosmic matter with a multiresolution decomposition. This is necessary in calculating the redshift distortion of power spectrum in the discrete wavelet transform (DWT)…
In this paper, we construct an algorithm for determining whether a given tessellation on a sphere is a spherical Laguerre Voronoi diagram or not. For spherical Laguerre tessellations, not only the locations of the Voronoi generators, but…
The Sloan Digital Sky Survey has obtained 450 square degrees of photometric scan data, in five bands (u',g',r',i',z'), which we use to identify clusters of galaxies. We illustrate how we do star-galaxy separation, and present a simple and…
We present a method which allows to extract theoretical informations out of a limited set of experimental data and observables, forming up in general an under- constrained system. It has been applied to the field of nucleon structure, in…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
Perturbation Theory (PT) applied to a cosmological density field with Gaussian initial fluctuations suggests a specific hierarchy for the correlation functions when the variance is small. In particular quantitative predictions have been…