Related papers: Percolation Statistics in the MillenniumTNG Simula…

Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…

We present density split statistics, a framework that studies lensing and counts-in-cells as a function of foreground galaxy density, thereby providing a large-scale measurement of both 2-point and 3-point statistics. Our method extends our…

The two point correlation function (2PCF) is a powerful statistical tool to measure galaxy clustering. Although 2PCF has also been used to study the clustering of stars on parsec and sub-parsec scales, its physical implication is not clear…

We present a comparison between two optical cluster finding methods: a matched filter algorithm using galaxy angular coordinates and magnitudes, and a percolation algorithm using also redshift information. We test the algorithms on two mock…

The developments summarized with the name ``weak gravitational lensing'' have led to exciting possibilities to study the (statistical properties of the) dark matter distribution in the Universe. Concentrating on those aspects which require…

(abridged) We use a theoretical model to predict the clustering properties of galaxy clusters. Our technique accounts for past light-cone effects on the observed clustering and follows the non-linear evolution of the dark matter correlation…

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 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…

We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of non-interacting line segments and disks in two spatial dimensions. These examples serve as models for…

Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…

Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…

Observations of the clustering of galaxies can provide useful information about the distribution of dark matter in the Universe. In order to extract accurate cosmological parameters from galaxy surveys, it is important to understand how the…

Imaging data from the Sloan Digital Sky Survey is used to measure the empirical size-richness relation for a large sample of galaxy clusters. Using population subtraction methods, we determine the radius at which the cluster galaxy number…

A lattice-based model for continuum percolation is applied to the case of randomly located, partially aligned sticks with unequal lengths in 2D which are allowed to cross each other. Results are obtained for the critical number of sticks…

The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…

In this paper we investigate the strong lensing statistics in galaxy clusters. We extract dark matter haloes from the Millennium-XXL simulation, compute their Einstein radius distribution, and find a very good agreement with Monte Carlo…

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…

Hierarchical structure formation leads to a clumpy distribution of dark matter in the Milky Way. These clumps are possible targets to search for dark matter annihilation with present and future $\gamma$-ray instruments. Many uncertainties…

Differences in clustering properties between galaxy subpopulations complicate the cosmological interpretation of the galaxy power spectrum, but can also provide insights about the physics underlying galaxy formation. To study the nature of…

Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…