Related papers: Probing Large Scale Structure using Percolation an…
The statistical analysis of cosmic large-scale structure is most often based on simple two-point summary statistics, like the power spectrum or the two-point correlation function of a sample of galaxies or other types of tracers. In…
We present a numerical study of topological descriptors of initially Gaussian and scale-free density perturbations evolving via gravitational instability in an expanding universe. We carefully evaluate and avoid numerical contamination in…
I outline the connections between some of the most widely used statistical measures of galaxy clustering and the fundamental issues in the theory of structure formation. I devote particular attention to the problem of biasing, i.e. to a…
This work explores the morphology and dynamical properties of cores within rich superclusters, highlighting their role as transitional structures in the large-scale structure of the Universe. Using projected and radial velocity…
We report a technique to calculate the impact of distinct physical processes inducing non-Gaussianity on the cosmological density field. A natural decomposition of the cosmic genus statistic into an orthogonal polynomial sequence allows…
I review recent progress in the study of the large-scale structure of the Universe through the distribution of clusters of galaxies, concentrating on new results using X-ray selected samples. After discussing the importance of understanding…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on…
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…
The gravitational evolution of the genus of the density field in large-scale structure is analytically studied in a weakly nonlinear regime using second-order perturbation theory. Weakly nonlinear evolution produces asymmetry in the…
This paper reviews selected aspects of the growth of cosmological structure, covering the following general areas: (1) expected characteristics of linear density perturbations according to various candidate theories for the origin of…
The magnification effects of clustered matter produce variations in the image sizes and number density of galaxies across the sky. This paper advocates the use of these effects in wide field surveys to map large-scale structure and the…
Future galaxy surveys hope to distinguish between the dark energy and modified gravity scenarios for the accelerating expansion of the Universe using the distortion of clustering in redshift space. The aim is to model the form and size of…
The topology of weak lensing fields is studied using the 2-dimensional genus statistic. Simulated fields of the weak lensing convergence are used to focus on the effect of nonlinear gravitional evolution and to model the statistical errors…
The genus statistics is studied using large $N$-body simulations for several cosmological models. We consider the effects of nonlinear gravitational evolution, smoothing the particle data in fully nonlinear regime, and the redshift-space…
Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…
In order to clarify how the percolation theory governs the conductivities in real materials which consist of small conductive particles, e.g., nanoparticles, with random configurations in an insulator, we numerically investigate the…
An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…