Related papers: Constructing, characterizing, and simulating Gauss…
I review recent progress in understanding and modeling galaxy clustering in cosmological simulations, with emphasis on models based on high-resolution dissipationless simulations. During the last decade, significant advances in our…
In this review, we describe our current understanding of cluster formation: from the general picture of collapse from initial density fluctuations in an expanding Universe to detailed simulations of cluster formation including the effects…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
Multivariate Gaussian distributions enjoy Gaussian conditional distributions that makes conditioning easy: conditioning boils down to implementing analytical formulae for conditional means and covariances. For more general distributions,…
Understanding the connection between galaxies and dark matter halos is a central challenge in modern cosmology. The Halo Occupation Distribution (HOD) framework provides a widely used statistical description of how galaxies populate dark…
We develop a simple, fast and predictive model of the hierarchical formation of galaxies which is in quantitative agreement with observations. Comparing simulations with observations we place constraints on the density of the universe and…
Motivated by observational results, we use IllustrisTNG hydrodynamical numerical simulations to study the alignment of the central galaxies in groups with the surrounding structures. This approach allows us to analyse galaxy and group…
Clusters traverse a gas and collide with gas particles. The gas particles are adsorbed and the clusters become hosts. If the clusters are size selected, the number of guests will be Poisson distributed. We review this by showcasing four…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
We investigate the performance of an analytic model of the 3D matter distribution, which combines perturbation theory with halo models, for weak-lensing configuration-space statistics. We compared our predictions for the weak-lensing…
The isothermal dynamical evolution of a clumpy and turbulent molecular cloud region and its fragmentation into a protostellar cluster is investigated numerically. The effect of different initial density and velocity distributions, generated…
I outline the connections between some of the most widely used statistical measures of galaxy clustering and the fundamental issues in the theory of structure formation. I devote particular attention to the problem of biasing, i.e. to a…
We follow the evolution of the galaxy population in a Lambda-CDM cosmology by means of high-resolution N-body simulations in which the formation of galaxies and their observable properties are calculated using a semi-analytic model. We…
Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating…
The modality is important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper we propose a new class of trimodal probability distributions, that is, probability distributions…
We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities,…
We study the evolution of the galactic globular cluster system to determine its initial mass-function and the fraction of halo stars that could have come from disrupted globular clusters. We study the cluster evolution under the influence…
Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
The current status of numerical simulations of galaxy formation is reviewed. After a short description of the main numerical simulation techniques, three sample applications illustrate how numerical simulations have provided deeper insight…