Related papers: Correlation function as a measure of the structure
We introduce the unbiased way statisticians look at the 2--point correlation function and study its relation to multifractal analysis. We apply this method to a simulation of the distribution of galaxy clusters in order to check the…
The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm…
Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses…
We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear…
We explore the scale and angular dependence of the cosmic shear three-point correlation function. The shear field is found to have a much more complex three-point function than the convergence field, but it also exhibits specific motifs…
Galaxy clustering and galaxy-galaxy lensing probe the connection between galaxies and their dark matter haloes in complementary ways. On one hand, the halo occupation statistics inferred from the observed clustering properties of galaxies…
We study biasing as a physical phenomenon by analysing power spectra (PS) and correlation functions (CF) of simulated galaxy samples and dark matter (DM) samples. We apply an algorithm based on the local densities of particles, $\rho$, to…
While galaxy cluster catalogs were compiled many decades ago, other structural elements of cosmic web are detected at definite level only in the newest works. For example, extragalactic filaments were described by velocity field and SDSS…
We investigate how well the redshift distributions of galaxies sorted into photometric redshift bins can be determined from the galaxy angular two-point correlation functions. We find that the uncertainty in the reconstructed redshift…
We present models for the three-point correlation function (3PCF) of both dark matter and galaxies. We show that models based on the halo model can reasonably match the dark matter 3PCF obtained from high-resolution $N$-body simulations. On…
Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…
We propose a method to probe higher-order correlators of the primordial density field through the inhomogeneity of local non-Gaussian parameters, such as f_NL, measured within smaller patches of the sky. Correlators between n-point…
Structural parameters of model star clusters are measured in radial profiles built from number-density, mass-density and surface-brightness distributions, assuming as well different photometric conditions. Star clusters of different ages,…
We study the space distribution of Abell and X-ray selected clusters of galaxies from the ROSAT Bright Source Catalog, and determine correlation functions for both cluster samples. On small scales the correlation functions depend on the…
The large-scale matter distribution represents a complex network of structure elements such as voids, clusters, filaments, and sheets. This network is spanned by a point distribution. The global properties of the point process can be…
Studying the structures (halos and galaxies) within the cosmic environments (void, sheet, filament, and node) where they reside is an ongoing attempt in cosmological studies. The link between the properties of structures and the cosmic…
The cosmological dark matter field is not completely described by its hierarchy of $N$-point functions, a non-perturbative effect with the consequence that only part of the theory can be probed with the hierarchy. We give here an exact…
The alignments between galaxies, their underlying matter structures, and the cosmic web constitute vital ingredients for a comprehensive understanding of gravity, the nature of matter, and structure formation in the Universe. We provide an…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
The morphological nature of structures that form under gravitational instability has been of central interest to cosmology for over two decades. A remarkable feature of large scale structures in the Universe is that they occupy a relatively…