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Theories of structure formation in a cold dark matter dominated Universe predict that massive clusters of galaxies assemble from the hierarchical merging of lower mass subhalos. Exploiting strong and weak gravitational lensing signals…
Higher-order statistics are a useful and complementary tool for measuring the clustering of galaxies, containing information on the non-gaussian evolution and morphology of large-scale structure in the Universe. In this work we present…
Continuous wavelet analysis has been increasingly employed in various fields of science and engineering due to its remarkable ability to maintain optimal resolution in both space and scale. Here, we introduce wavelet-based statistics,…
Many approaches to obtaining cosmological constraints rely on the connection between galaxies and dark matter. However, the distribution of galaxies is dependent on their formation and evolution as well as the cosmological model, and galaxy…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
We use very large cosmological N--body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM)…
The angular correlation is a method for measuring the distribution of structure in the Universe, through the statistical properties of the angular distribution of galaxies on the sky. We measure the angular correlation of galaxies from the…
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…
In non-linear scales, the matter density distribution is not Gaussian. Consequently, the widely used two-point correlation function is not adequate anymore to capture the matter density field's entire behaviour. Among all statistics beyond…
Connecting galaxies with their descendants (or progenitors) at different redshifts can yield strong constraints on galaxy evolution. Observational studies have historically selected samples of galaxies using a physical quantity, such as…
We calculated spatial correlation functions of galaxies, $\xi(r)$, structure functions, $g(r)=1 +\xi(r)$, gradient functions, $\gamma(r)= d \log g(r)/ d \log r$, and fractal dimension functions, $D(r)= 3+\gamma(r)$, using dark matter…
Hydrodynamical simulations of galaxy formation have now reached sufficient volume to make precision predictions for clustering on cosmologically relevant scales. Here we use our new IllustrisTNG simulations to study the non-linear…
We produce mock angular catalogues from simulations with different initial power spectra to test methods that recover measures of clustering in three dimensions, such as the power spectrum, variance and higher order cumulants. We find that…
In recent years, deep learning approaches have achieved state-of-the-art results in the analysis of point cloud data. In cosmology, galaxy redshift surveys resemble such a permutation invariant collection of positions in space. These…
We present a preliminary study exploring whether the stellar orbital circularity of simulated galaxies, available from precomputed catalogs in the IllustrisTNG project, can be used as a proxy for broad morphological classification. We focus…
Although coherent large-scale structures such as filaments and walls are apparent to the eye in galaxy redshift surveys, they have so far proven difficult to characterize with computer algorithms. This paper presents a procedure that uses…
Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small…
Current models of galaxy formation applied to understanding the large-scale structure of the universe have two parts. The first is an accurate solution of the equations of motion for the dark matter due to gravitational clustering. The…
The correlation function of galaxy clusters has often been used as a test of cosmological models. A number of assumptions are implicit in the comparison of theoretical expectations to data. Here we use an ensemble of ten large N-body…
The alignment of clusters of galaxies with their nearest neighbours and between clusters within a supercluster is investigated using simulations of 512^{3} dark matter particles for \LambdaCDM and \tauCDM cosmological models. Strongly…