Related papers: Multiscale Methods
Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy…
We suggest a two-dimensional wavelet devised to deduce the large-scale structure of a physical field (e.g., the Galactic magnetic field) from its integrals along straight paths from irregularly spaced data points to a fixed interior point…
We have developed a method based on wavelets to obtain the true underlying smooth density from a point distribution. The goal has been to reconstruct the density field in an optimal way ensuring that the morphology of the reconstructed…
Many statistical methods have been proposed in the last years for analyzing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex observational sample volumes. In this paper, we…
These lectures cover various aspects of the statistical description of cosmological density fields. Observationally, this consists of the point process defined by galaxies, and the challenge is to relate this to the continuous density field…
We apply the scale-length method to several three dimensional samples of the Two degree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies…
We discuss the galaxy clustering based on thermodynamics and statistical mechanics in the expanding universe in a modified theory of gravity. The modified general relativity (MGR) is developed using the regular line element field to…
Modeling the mass distribution of galaxy-scale strong gravitational lenses is a task of increasing difficulty. The high-resolution and depth of imaging data now available render simple analytical forms ineffective at capturing lens…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
These are advanced lecture notes covering recent developments in the methodology used to analyse galaxy surveys. The focus is particularly on direct measurements of the galaxy power spectrum although I also discuss its Fourier transform,…
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological…
The large-scale structure in cosmology is highly non-Gaussian at late times and small length scales, making it difficult to describe analytically. Parameter inference, data reconstruction, and data generation tasks in cosmology are greatly…
Pressing questions in cosmology such as the nature of dark matter and dark energy can be addressed using large galaxy surveys, which measure the positions, properties and redshifts of galaxies in order to map the large-scale structure of…
Wavelet analysis is proposed as a new tool for studying the large-scale structure formation of the universe. To reveal its usefulness, the wavelet decomposition of one-dimensional cosmological density fluctuations is performed. In contrast…
These lectures deal with our current knowledge of the matter distribution in the universe, focusing on how this is studied via the large-scale structure seen in galaxy surveys. We first assemble the necessary basics needed to understand 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…
Large-scale structure (LSS) analysis in galaxy surveys is a powerful cosmological probe but is limited by tracer bias, which can obscure underlying information and weaken parameter constraints. Existing methods either model bias or restrict…
This document describes analytical and numerical techniques for the generation of Gaussian density fields, which represent cosmological density perturbations. The mathematical techniques involved in the generation of density harmonics in…
In this introductory talk we will establish connections between the statistical analysis of galaxy clustering in cosmology and recent work in mainstream spatial statistics. The lecture will review the methods of spatial statistics used by…
Intriguing parallels between density fluctuation power versus wavenumber on small (mm) and large (Mpc) scales are presented. The comparative study is carried out between fusion plasma measurements and cosmological data. Based on predictions…