Related papers: The supercluster--void network III. The correlatio…
We present the first measurement of the angular correlation function in a $K$-selected galaxy survey, from two fields covering almost 10 square degrees. The angular correlation function at small angles is well described by a $\theta^{-0.8}$…
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…
This paper reviews the measurements of galaxy correlations at high redshifts, and discusses how these may be understood in models of hierarchical gravitational collapse. The clustering of galaxies at redshift one is much weaker than at…
Percolation, a paradigmatic geometric system in various branches of physical sciences, is known to possess logarithmic factors in its correlators. Starting from its definition, as the $Q\rightarrow1$ limit of the $Q$-state Potts model with…
We show that the galaxy correlation function does not evolve in proportion with the correlation function of the underlying mass distribution. Earliest galaxies cluster very strongly and the amplitude of the galaxy correlation function…
Transient dynamics leading to the synchrony of pulse-coupled oscillators has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the…
Measurements of the peculiar velocities of large samples of galaxies enable new tests of the standard cosmological model, including determination of the growth rate of cosmic structure that encodes gravitational physics. With the size of…
The steady state reached by a system of particles sliding down a fluctuating surface has interesting properties. Particle clusters form and break rapidly, leading to a broad distribution of sizes and large fluctuations. The density-density…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
Forthcoming galaxy surveys will provide measurements of galaxy clustering with an unprecedented level of precision, that will require comparably good accuracy. Current models for galaxy correlations rely on approximations and idealizations…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
We perform a statistical study focused on void environments. We examine galaxy density profiles around voids in the SDSS, finding a correlation between void--centric distance to the shell of maximum density and void radius when a maximum in…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
We use the two-point correlation function in redshift space, $\xi(s)$, to study the clustering of the galaxies and groups of the Nearby Optical Galaxy (NOG) Sample, which is a nearly all-sky, complete, magnitude-limited sample of \~7000…
The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two…
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial…
Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we…
I compare various semi-analytic models for the bias of dark matter halos with halo clustering properties observed in recent numerical simulations. The best fitting model is one based on the collapse of ellipsoidal perturbations proposed by…
The influence of large-scale density fluctuations on structure formation on small scales is described by the three-point correlation function (bispectrum) in the so-called "squeezed configurations," in which one wavenumber, say $k_3$, is…
We present a comparison of the predictions of perturbation theory for the hierarchical J-order correlation amplitudes $S_J=\xibar_J/\xibar_2^{J-1}$, $J=3-10$, with the results of large numerical simulations of gravitational clustering. We…