Related papers: Quantifying galactic clustering and departures fro…
This review presents a comprehensive overview of galaxy bias, that is, the statistical relation between the distribution of galaxies and matter. We focus on large scales where cosmic density fields are quasi-linear. On these scales, the…
The major uncertainties in studies of the multi-scale structure of the Universe arise not from observational errors but from the variety of legitimate definitions and detection methods for individual structures. To facilitate the study of…
Using two-dimensional numerical simulations of gravitational clustering, with initial power spectra of a power-law form with index n, we compare the properties of voids in real space to their properties in redshift space. Both the void…
We introduce new statistical methods for the study of cosmic voids, focusing on the statistics of largest size voids. We distinguish three different types of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
We relate the information entropy and the mass variance of any distribution in the regime of small fluctuations. We use a set of Monte Carlo simulations of different homogeneous and inhomogeneous distributions to verify the relation and…
This paper presents a new derivation of the Generalized Poisson distribution. This distribution provides a good fit to the evolved, counts-in-cells distribution measured in numerical simulations of hierarchical clustering from Poisson…
CONTEXT: Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect…
Markov Random Field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In…
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe.…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
Galaxy bias, the unknown relationship between the clustering of galaxies and the underlying dark matter density field is a major hurdle for cosmological inference from large-scale structure. While traditional analyses focus on the absolute…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
The properties of large underdensities in the distribution of galaxies in the Universe, known as cosmic voids, are potentially sensitive probes of fundamental physics. We use data from the MultiDark suite of N-body simulations and multiple…
Mismodeling the uncertain, diffuse emission of Galactic origin can seriously bias the characterization of astrophysical gamma-ray data, particularly in the region of the Inner Milky Way where such emission can make up over 80% of the photon…
Motivated by the fundamental problem of modeling the frequency of frequencies (FoF) distribution, this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random…
The statistical properties of cosmic structures are well known to be strong probes for cosmology. In particular, several studies tried to use the cosmic void counting number to obtain tight constrains on Dark Energy. In this paper we…
Data which lie in the space $\mathcal{P}_{m\,}$, of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications including medical imaging, computer vision, and radar signal…
The space of probability densities is an infinite-dimensional Riemannian manifold, with Riemannian metrics in two flavors: Wasserstein and Fisher--Rao. The former is pivotal in optimal mass transport (OMT), whereas the latter occurs in…
The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a…