Related papers: The supercluster--void network III. The correlatio…
In non-linear scales, the matter density distribution is not Gaussian. Consequently, the widely used two-point correlation function is not adequate anymore to capture the matter density field's entire behaviour. Among all statistics beyond…
We study linear relations among correlation functions on a lattice obtained from integration-by-parts identities. We use the framework of twisted cocycles and determine for a scalar theory a basis of correlation functions, in which all…
Variations in the number of globular clusters per unit galaxy luminosity, which is the specific frequency, and the mass of globular clusters per unit total available mass, are reviewed. Correlations with galaxy luminosity and morphology,…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
The large-scale structure of the Universe is thought to evolve by a process of gravitational amplification from low-amplitude Gaussian noise generated in the early Universe. The later, non-linear stages of gravitation-induced clustering…
The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the…
Stars form predominantly in groups usually denoted as clusters or associations. The observed stellar groups display a broad spectrum of masses, sizes and other properties, so it is often assumed that there is no underlying structure in this…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
We probe gravitational clustering in N-body simulations using geometrical descriptors sensitive to `connectedness': the genus curve, percolation and shape statistics. We find that both genus and percolation curves provide complementary…
The large-scale structure of the universe can only be observed via luminous tracers of the dark matter. However, the clustering statistics of tracers are biased and depend on various properties, such as their host-halo mass and assembly…
We determine the evolution from $z=3\to 0$ of the galaxy and mass correlation functions and bias factor in a $50h^{-1}$Mpc $\Lambda$CDM hydrodynamic simulation with $10h^{-1}$kpc resolution. The mass correlation function grows with time,…
Aims. We investigate how properties of the ensemble of superclusters in the cosmic web evolve with time. Methods. We perform numerical simulations of the evolution of the cosmic web using the LambdaCDM model in box sizes L0 = 1024, 512, 256…
I review the status of large-scale structure studies based on redshift surveys of galaxies and clusters of galaxies. In particular, I compare recent results on the power spectrum and two-point correlation correlation function from the 2dF…
I present here a review of Large-Scale Structure (LSS) studies using clusters of galaxies. First, I re-evaluate the `pros' and `cons' of using clusters for such studies, especially in this era of large galaxy redshift surveys. Secondly, I…
We measure the topology of the main galaxy distribution using the Seventh Data Release of the Sloan Digital Sky Survey, examining the dependence of galaxy clustering topology on galaxy properties. The observational results are used to test…
The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
An energy eigenfunction in a classically chaotic system is known to have spatial correlations which (in the limit of small $\hbar$) are governed by a microcanonical distribution in the classical phase space. This result is valid, however,…
We show that scale-scale correlations are a generic feature of slow-roll inflation theories. These correlations result from the long-time tails characteristic of the time dependent correlations because the long wavelength density…