Related papers: Zipf's law for fractal voids and a new void-finder
Voids are a prominent feature of the galaxy distribution but their quantitative study is hindered by the lack of a precise definition of what constitutes a void. Here we propose a definition of voids in point distributions that uses methods…
We study here, from first principles, what properties of voids are to be expected in a fractal point distribution and how the void distribution is related to its morphology. We show this relation in various examples and apply our results to…
"Cut-out sets" are fractals that can be obtained by removing a sequence of disjoint regions from an initial region of d-dimensional euclidean space. Conversely, a description of some fractals in terms of their void complementary set is…
Voids are the most prominent feature of the LSS of the universe. Still, they have been generally ignored in quantitative analysis of it, essentially due to the lack of an objective tool to identify and quantify the voids. To overcome this,…
This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications…
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…
In this review we discuss several aspects of Cosmic Voids. Voids are a major component of the large scale distribution of matter and galaxies in the Universe. They are of instrumental importance for understanding the emergence of the Cosmic…
A method for detecting voids in the galaxy distribution is presented. Using this method, we have identified 732 voids with a radius of the seed sphere Rseed > 4.0h^{-1}Mpc in a volume-limited sample of galaxies from the southern part of the…
Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of…
We introduce new statistical methods for the study of cosmic voids, focusing on the statistics of largest size voids. We distinguish three different types of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
The voids between galaxies are identified with the volumes of the Poisson Voronoi tessellation. Two new survival functions for the apparent radii of voids are derived. The sectional normalized area of the Poisson Voronoi tessellation is…
Voids are the most prominent feature of the large-scale structure of the universe. Still, they have been generally ignored in quantitative analysis of it, essentially due to the lack of an objective tool to identify the voids and to…
Under the assumption of a void-filled Universe we investigate if the characteristic scale of voids can be determined from existing surveys. We use the Voronoi tessellation to create mock surveys and study the properties of the first…
Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of…
Cosmic voids are effective cosmological probes to discriminate among competing world models. Their identification is generally based on density or geometry criteria that, because of their very nature, are prone to shot noise. We propose two…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
The major uncertainties in studies of the multi-scale structure of the Universe arise not from observational errors but from the variety of legitimate definitions and detection methods for individual structures. To facilitate the study of…
We introduce Void Hierarchy as an important property of the Large--Scale Structure in the Universe and demonstrate how it can be used to interpret observations. Moreover the void hierarchy constraints any realistic galaxy and structure…