Related papers: Multiscale Methods
In this manuscript I review the mathematics and physics that underpins recent work using the clustering of galaxies to derive cosmological model constraints. I start by describing the basic concepts, and gradually move on to some of the…
Key non-Gaussian properties of cosmological fields can be captured by their one-point statistics, providing a complement to two-point statistical measurements from power spectra or correlation functions. Large deviation theory can robustly…
A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material…
This paper presents a completely analytic treatment of cosmological fluctuations whose wavelength is small enough to come within the horizon well before the energy densities of matter and radiation become equal. This analysis yields a…
Gauss-Hermite and Gauss-Laguerre ("shapelet") decompositions of images have become important tools in galaxy modeling, particularly for the purpose of extracting ellipticity and morphological information from astronomical data. However, the…
This article is a tutorial on the practical implementation of a method of measurement of minute deformations based on multiple scattering. This technic has been recently developed and has proven to give new insights on the spatial…
We revise and extend the stochastic approach to cumulative weak lensing (hereafter the sGL method) first introduced in Ref. [1]. Here we include a realistic halo mass function and density profiles to model the distribution of mass between…
This course presents some applications of gravitational lensing to the measurement of masses of galaxies (galaxy-galaxy lensing, Eintein rings, perturbations of giant arcs) and cluster of galaxies (strong and weak lensing). This complements…
Starting with a `bare' 4-dimensional differential manifold as a model of spacetime, we discuss the options one has for defining a volume element which can be used for physical theories. We show that one has to prescribe a scalar density…
The different regimes of gravitational lensing constitutes an interesting tool in order to map the mass distribution in galaxy clusters on different scales. In this proceedings article, I review some work I have performed on this topic.…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
We use continuous wavelet transform techniques to construct the global and environment-dependent wavelet statistics, such as energy spectrum and kurtosis, to study the fluctuation and intermittency of the turbulent motion in the cosmic…
Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths.…
We construct a two-field higher-order gradient micropolar model for Cosserat media on the basis of a square lattice of elements with rotational degrees of freedom. This model includes equations of single-field higher-order gradient…
Modern galaxy surveys focus on the galaxy power spectrum or 2-point correlation function to test and constrain cosmological models. Additional information comes from higher-order N-point functions, but their analysis is challenging. A…
The early universe provides an opportunity for quantum gravity to connect to observation by explaining the large-scale structure of the Universe. In the group field theory (GFT) approach, a macroscopic universe is described as a GFT…
We review recent advancements in cosmology with galaxy clusters. Galaxy clusters are the most massive objects in the Universe. Consequently the cluster number density as a function of cluster mass, or cluster abundance, is sensitive to…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
In this pedagogical lecture, I introduce some of the basic terminology and description of fluctuating fields as they occur on cosmology. I define various statistical, cosmological and sample homogeneity and explain what is meant by the fair…
This article discusses various methods of representing and manipulating arbitrary coverage information in two dimensions, with a focus on space- and time-efficiency when processing such coverages, storing them on disk, and transmitting them…