Related papers: The Two--Point Correlation Function and the Size o…
3D Voronoi's tessellation method was first applied to identify groups of galaxies in the structure of a supercluster. The sample under consideration consists of more than 7000 galaxies of the Local Supercluster (LS) with radial velocities…
On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its…
Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…
In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of…
One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determine the shape of the correlation function, its possible evolution…
We show how a characteristic length scale imprinted in the galaxy two-point correlation function, dubbed the "linear point", can serve as a comoving cosmological standard ruler. In contrast to the Baryon Acoustic Oscillation peak location,…
The 3D network originated by the faces of irregular Poissonian Voronoi Polyhedrons may represent the backbone on which the galaxies are originated. As a consequence the spatial appearance of the catalogs of galaxies can be reproduced. The…
The 2-point correlation function of the galaxy spatial distribution is a major cosmological observable that enables constraints on the dynamics and geometry of the Universe. The Euclid mission aims at performing an extensive spectroscopic…
The most popular tools for analysing the large scale distribution of galaxies are second-order spatial statistics such as the two-point correlation function or its Fourier transform, the power spectrum. In this review, we explain how our…
The expanding complex pattern of filaments, walls and voids build the evolving cosmic web with material flowing from underdense onto high density regions. Here we explore the dynamical behaviour of voids and galaxies in void shells relative…
We study the Voronoi and void statistics of super-homogeneous (or hyperuniform) point patterns in which the infinite-wavelength density fluctuations vanish. Super-homogeneous or hyperuniform point patterns arise in one-component plasmas,…
We study scaling behaviour of statistics of voids in the context of the halo model of nonlinear large-scale structure. The halo model allows us to understand why the observed galaxy void probability obeys hierarchical scaling, even though…
A general method is proposed for predicting the asymptotic percolation threshold of networks with bottlenecks, in the limit that the sub-net mesh size goes to zero. The validity of this method is tested for bond percolation on filled…
This work describes a full Bayesian analysis of the Nearby Universe as traced by galaxies of the 2M++ survey. The analysis is run in two sequential steps. The first step self-consistently derives the luminosity dependent galaxy biases, the…
Aims: We assess the sensitivity of void shapes to the nature of dark energy that was pointed out in recent studies. We investigate whether or not void shapes are useable as an observational probe in galaxy redshift surveys. We focus on the…
We consider the two-point correlation function of the photodissociation cross section in molecules where the fragmentation process is indirect, passing through resonances above the dissociation threshold. In the limit of overlapping…
Despite a history that dates back at least a quarter of a century studies of voids in the large--scale structure of the Universe are bedevilled by a major problem: there exist a large number of quite different void--finding algorithms, a…
The properties of the galaxy distribution at large scales are usually studied using statistics which are assumed to be self-averaging inside a given sample. We present a new analysis able to quantitatively map galaxy large scale structures…
The void power spectrum is related to the clustering of low-density regions in the large-scale structure (LSS) of the Universe, and can be used as an effective cosmological probe to extract the information of the LSS. We generate the galaxy…
We have used integral two-point spatial correlation function and its second derivative to analyze the distribution of quasars in three very deep surveys published in the literature. Statistically significant ($\sim 2-3\sigma $) correlations…