Related papers: Scaling in Gravitational Clustering, 2D and 3D Dyn…
The 1-point matter density probability distribution function (PDF) captures some of the non-Gaussian information lost in standard 2-point statistics. The matter PDF can be well predicted at mildly non-linear scales using large deviations…
Context: Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF). In order to successfully exploit such observables, a detailed…
We present a first principle approach to obtain analytical predictions for spherically-averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation…
We introduce the position-dependent probability distribution function (PDF) of the smoothed matter field as a cosmological observable. In comparison to the PDF itself, the spatial variation of the position-dependent PDF is simpler to model…
The probability density function (PDF) of velocity fluctuations is studied experimentally for grid turbulence in a systematical manner. At small distances from the grid, where the turbulence is still developing, the PDF is sub-Gaussian. At…
We study local power fluctuations in numerical simulations of stationary, homogeneous, isotropic turbulence in two and three dimensions with Gaussian forcing. Due to the near-Gaussianity of the one-point velocity distribution, the…
We investigate the single-point velocity probability density function (PDF) in three-dimensional fully developed homogeneous isotropic turbulence within the framework of PDF equations focussing on deviations from Gaussianity. A joint…
The evolution of probability distribution functions (PDFs) of continuous density, velocity and velocity derivatives ( deformation tensor) fields in the theory of cosmological gravitational instability are considered. We show that in the…
We calculate the lowest-order non-linear contributions to the power spectrum, two-point correlation function, and smoothed variance of the density field, for Gaussian initial conditions and scale-free initial power spectra, $P(k) \sim k^n$.…
Cosmological Perturbation Theory (PT) is a useful tool to study the cumulants of the density and velocity fields in the large scale structure of the Universe. In Papers I & II of this series we saw that the Spherical Collapse (SC) model…
We present non-linear solutions of Vlasov Perturbation Theory (VPT), describing gravitational clustering of collisionless dark matter with dispersion and higher cumulants induced by orbit crossing. We show that VPT can be cast into a form…
In performing cosmological N-body simulations, it is widely appreciated that the growth of structure on the largest scales within a simulation box will be inhibited by the finite size of the simulation volume. Following ideas set forth in…
The Velocity Gradients Technique (VGT) and the Probability Density Functions (PDFs) of mass density are tools to study turbulence, magnetic fields, and self-gravity in molecular clouds. However, self-absorption can significantly make the…
The gravitational evolution of the cosmic one-point probability distribution function (PDF) has been estimated using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion around a Gaussian…
Weak lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps. The probability distribution (PDF)…
Using an ensemble of high resolution 2D numerical simulations, we explore the scaling properties of cosmological density fluctuations in the non-linear regime. We study the scaling behaviour of the usual $N$--point volume-averaged…
In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…
We present results of the investigations of the statistical properties of a joint density and velocity divergence probability distribution function (PDF) in the mildly non-linear regime. For that purpose we use both perturbation theory…
This work reports on the application of the Eulerian perturbation theory to a recently proposed model of cosmological structure formation by gravitational instability (astro-ph/0009414). Its physical meaning is discussed in detail and put…
We study the possibility of using the entire probability distribution function (PDF) of the aperture mass Map and its related cumulative probability distribution function (CPDF) to obtain meaningful constraints on cosmological parameters.…