Related papers: Some Statistics for Measuring Large-Scale Structur…
We extend our earlier study about the fractional exclusion statistics to higher dimensions in full physical range and in the non-relativistic and ultra-relativistic limits. Also, two other fractional statistics, namely Gentile and…
The formation and evolution of galaxies cannot be separated from large scale structure growth. Dark matter halos (and, therefore, galaxies) form and grow within the cosmic web - the classification of large-scale structure as distinct…
The clustering amplitude of galaxies depends on their intrinsic luminosity. We compare the properties of publicly available galaxy formation models with clustering measurements from the two-degree field galaxy redshift survey. The model…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
In recent years, unprecedented progress in observational cosmology has revealed a great deal of information about the formation and evolution of structures in the universe. This, in turn, has raised many challenging issues for the…
We present in this paper a quantitative method for defining void size in large-scale structure based on percolation threshold density. Beginning with two-dimensional gravitational clustering simulations smoothed to the threshold of…
Clustering of large-scale structure provides significant cosmological information through the power spectrum of density perturbations. Additional information can be gained from higher-order statistics like the bispectrum, especially to…
We describe cosmological simulation techniques and their application to studies of cosmic structure formation, with particular attention to recent hydrodynamic simulations of structure in the high redshift universe. Collisionless N-body…
The growth rate of cosmic structure is a powerful cosmological probe for extracting information on the gravitational interactions and dark energy. In the late time Universe, the growth rate becomes non-linear and is usually probed by…
QSOs and radio-galaxies, together with the CMB, ``normal'' galaxies and clusters, represent the main source of information about the origin and evolution of the Large Scale Structure. They can be used either directly, as tracers of the…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
The genus of the iso-density contours is a robust measure of the topology of large scale structure, and it is relatively insensitive to nonlinear gravitational evolution, galaxy bias and redshift-space distortion. We show that the growth of…
The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit…
It is shown that the evolution of the density perturbations during certain eras of substantial entropy generation in the universe can be described in the scheme of the KPZ equation. Therefore, the influence on cosmological structure…
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…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
A new way of probing the large-scale structure of the universe is proposed. Space is partitioned into cells the shape of rhombic dodecahedron. The cells are labelled ``filled'' or ``empty'' according as they contain galaxies or not. The…
A field theory with generalized statistics in one space dimension is introduced. The statistics enters the scene through the coupling of the matter fields to a statistical gauge field, as it happens in the Chern-Simons theory in two…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…