Related papers: The Two--Point Correlation Function and the Size o…
The size of the horizon at the matter-radiation equality is a key scale of the Big Bang cosmology that is directly related to the energy-matter content of the Universe. In this letter, we argue that this scale can be accurately measured…
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…
We present new estimates of the spatial two-point correlation function of rich clusters of galaxies selected from the APM Galaxy Survey. We have measured redshifts for a sample of $364$ clusters out to a depth of $\sim 450\hmpc$. The…
We present simulations of a cosmic shear survey and show how the survey geometry influences the accuracy of determination of cosmological parameters. We numerically calculate the full covariance matrices Cov of two-point statistics of…
We revisit a new type of a Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, and analyze the structure and complexity of the…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
Using cosmological $N$-body simulations and the void probability function (VPF), we investigate the statistical properties of voids within a wide range of initially Gaussian models for the origin of large-scale structure. We pay particular…
Second-order measures, such as the two-point correlation function, are geometrical quantities describing the clustering properties of a point distribution. In this article well-known estimators for the correlation integral are reviewed and…
We stress the importance of stochastic geometry as a branch of mathematical statistics particularly suited to model and investigate nontrivial spatial patterns. One of its key concepts, Voronoi tessellations, represents a versatile and…
We measure the distribution of matter contained within the emptiest regions of the Universe: cosmic voids. We use the large overlap between the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS) and voids identified in the LOWZ and…
The large under-dense regions in the cosmological matter density field, known as cosmic voids, are powerful probes of cosmology but their potential is currently under-exploited. Observationally, voids are identified within the large scale…
Cosmic voids are underdense regions within the large-scale structure of the Universe, spanning a wide range of physical scales - from a few megaparsecs (Mpc) to the largest observable structures. Their distinctive properties make them…
We study how well void-finding algorithms identify cosmic void regions and whether we can quantitatively and qualitatively compare the voids they find with dynamical information from the underlying matter distribution. Using the ORIGAMI…
Cosmic voids are a key component of the large-scale structure that contain a plethora of cosmological information. Typically, voids are identified from the underlying galaxy distribution, which is a biased tracer of the total matter field.…
2-point topological charge correlation functions of several types of geometric singularity in gaussian random fields are calculated explicitly, using a general scheme: zeros of $n$-dimensional random vectors, signed by the sign of their…
We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities,…
The intrinsic alignments of galaxies, i.e., the correlation between galaxy shapes and their environment, are a major source of contamination for weak gravitational lensing surveys. Most studies of intrinsic alignments have so far focused on…
We explore the morphology of galaxies living in the proximity of cosmic voids, using a sample of voids identified in the Sloan Digital Sky Survey Data Release 7. At all stellar masses, void galaxies exhibit morphologies of a later type than…
Voids are a dominant feature of the low-redshift galaxy distribution. Several recent surveys have found evidence for the existence of large-scale structure at high redshifts as well. We present analytic estimates of galaxy void sizes at…
Voronoi tessellation, also known as Voronoi diagram, is an important computational geometry technique that has applications in various scientific disciplines. It involves dividing a given space into regions based on the proximity to a set…