Related papers: Constructing, characterizing, and simulating Gauss…
We study cell count moments up to fifth order of the distributions of haloes, of halo substructures as a proxy for galaxies, and of mass in the context of the halo model and compare theoretical predictions to the results of numerical…
We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…
Understanding $\textit{galaxy bias}$ -- that is the statistical relation between matter and galaxies -- is of key importance for extracting cosmological information from galaxy surveys. While the bias function $f$ -- that is the probability…
We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
We consider the Voronoi tessellation based on a homogeneous Poisson point process in $\mathbf{R}^{d}$. For a geometric characteristic of the cells (e.g. the inradius, the circumradius, the volume), we investigate the point process of the…
We perform a quantitative comparison between N-body simulations and the Schr\"odinger-Poisson system in 1+1 dimensions. In particular, we study halo formation with different initial conditions. We observe the convergence of various…
Small- and intermediate-scale galaxy clustering can be used to establish the galaxy-halo connection to study galaxy formation and evolution and to tighten constraints on cosmological parameters. With the increasing precision of galaxy…
The one-point probability distribution function (pdf) is computed for the $25\hmpc$-smoothed density field of rich clusters of galaxies in the Abell/\aco\ catalogs. The observed pdf is compared to the pdf s drawn similarly from mock…
The observed clustering of galaxies and the cross-correlation of galaxies and mass provide important constraints on both cosmology and models of galaxy formation. Even though the dissipation and feedback processes associated with galaxy…
We study the dependence on configuration in momentum space of the primordial 3-point function of density perturbations in several different scenarios: standard slow-roll inflation, curvaton and variable decay models, ghost inflation, models…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
Large-scale structure of Universe includes galaxy clusters connected by filaments. Voids occupy the rest of cosmic volume. The search of any dependencities in filament structure can give answer to more general questions about origin of…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
In these lecture notes, we describe the current state-of-the-art for numerical simulations of large-scale structure and galaxy formation. Numerical simulations play a central role in the preparation and the exploitation of large-scale…
The dependence of galaxy clustering on local density provides an effective method for extracting non-Gaussian information from galaxy surveys. The two-point correlation function (2PCF) provides a complete statistical description of a…
In the peaks approach, the formation sites of observable structures in the Universe are identified as peaks in the matter density field. The statistical properties of the clustering of peaks are particularly important in this respect. In…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Starting from first principles, we derive the fundamental equations that relate the $n$-point correlation functions in real and redshift space. Our result generalises the so-called `streaming model' to higher-order statistics: the full…
Gravitational lensing allows to quantify the angular distribution of the convergence field around clusters of galaxies to constrain their connectivity to the cosmic web. We describe in this paper the corresponding theory in Lagrangian space…