Related papers: Analysis of Large Scale Structure using Percolatio…
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…
By virtue of their high galaxy space densities and their large spatial separations, clusters are efficient and accurate tracers of the large-scale density and velocity fields. Substantial progress has been made over the past decade in the…
The cosmic large scale structure encodes the formation and evolution of a weblike network of dark matter and galaxies within the Universe. The cosmological information is wrapped up in non-Gaussian statistics requiring characterisation…
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…
[Abridged] We consider how galaxy clustering data, from Mpc to Gpc scales, from upcoming large scale structure surveys, such as Euclid and DESI, can provide discriminating information about the bispectrum shape arising from a variety of…
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 review a range of stastistical methods for analyzing the structures of star clusters, and derive a new measure ${\cal Q}$ which both quantifies, and distinguishes between, a (relatively smooth) large-scale radial density gradient and…
The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations…
Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Although coherent large-scale structures such as filaments and walls are apparent to the eye in galaxy redshift surveys, they have so far proven difficult to characterize with computer algorithms. This paper presents a procedure that uses…
We develop the formalism to include substructure in the halo model of clustering. Real halos are not likely to be perfectly smooth, but have substructure which has so far been neglected in the halo model -- our formalism allows one to…
We apply Shapefinders, statistical measures of `shape' constructed from two dimensional partial Minkowski functionals, to study the degree of filamentarity in the Las Campanas Redshift Survey (LCRS). In two dimensions, three Minkowski…
To explain the rich structure of voids, clusters, sheets, and filaments apparent in the Universe, we present evidence for the convergence of the two classic approaches to gravitational clustering, the ``pancake'' and ``hierarchical''…
Minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size, shape and connectivity. Here we point out, that these scalar descriptors can be complemented by vector-valued curvature…
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
The interstellar medium is highly structured, presenting a range of morphologies across spatial scales. The large data sets resulting from observational surveys and state-of-the-art simulations studying these hierarchical structures means…
We use the Millennium Simulation, a 10 billion particle simulation of the growth of cosmic structure, to construct a new model of galaxy clustering. We adopt a methodology that falls midway between the traditional semi-analytic approach and…
The history and the major results of the study of the topology of the large-scale structure are briefly reviewed. Two techniques based on percolation theory and the genus curve are discussed. The preliminary results of the percolation…
We study the substructure statistics of a representative sample of galaxy clusters by means of two currently popular substructure characterisation methods, power ratios and centroid shifts. We use the 31 clusters from the REXCESS sample,…