Related papers: Genus Statistics of the Large-Scale Structure with…
We developed an optimal in the natural sense algorithm of partition in cluster analysis based on the densities of observations in the different hypotheses. These densities may be characterized, for instance, as the multivariate so-called…
We develop a field-theoretic description of large-scale structure formation by taking the non-relativistic limit of a canonically transformed, real scalar field which is minimally coupled to scalar gravitational perturbations in…
A quantitative theory, based on the Zeldovich approximation, to provide an approximate description of the evolution of structure is presented. We give an expression for the characteristic scale of superlarge-scale structure which can also…
We study the topology of the matter density field in two dimensional slices, and consider how we can use the amplitude $A$ of the genus for cosmological parameter estimation. Using the latest Horizon Run 4 simulation data, we calculate the…
We consider the problem of calculating the Gaussian curvature of a conical 2-dimensional space by using concepts and techniques of distribution theory. We apply the results obtained to calculate the Riemannian curvature of the 4-dimensional…
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…
Non-Gaussian statistics in the distribution of large scale structure, and in temperature fluctuations of the cosmic microwave background, can be used to constrain inflationary models. Data on the cosmic microwave background from Planck…
We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies…
The skeleton formalism aims at extracting and quantifying the filamentary structure of the universe is generalized to 3D density fields; a numerical method for computating a local approximation of the skeleton is presented and validated…
A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…
We discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(>>1)-dimensional Gaussian landscape. The particular attention is paid to the case of landscapes with…
We present forecast results for constraining the primordial non-Gaussianity from photometric surveys through a large-scale enhancement of the galaxy clustering amplitude. In photometric surveys, the distribution of observed galaxies at high…
I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random…
Perturbations in a universe with matter and cosmological constant are computed in terms of the primordial scalar perturbation up to second order. The calculation is easy -- a generalization of the spherical dust solution. Our expression…
This paper introduces chi-square goodness-of-fit tests to check for conditional distribution model specification. The data is cross-classified according to the Rosenblatt transform of the dependent variable and the explanatory variables,…
We calculate curvature perturbations in the scenario in which the curvaton field decays into another scalar field via parametric resonance. As a result of a nonlinear stage at the end of the resonance, standard perturbative calculation…
Current tools for multivariate density estimation struggle when the density is concentrated near a nonlinear subspace or manifold. Most approaches require choice of a kernel, with the multivariate Gaussian by far the most commonly used.…
The quantum theory of the electromagnetic field enables the description of multiphoton states exhibiting nonclassical statistical properties, often reflected in non-Gaussian phase-space distributions. While non-Gaussianity alone does not…
We present an application of Large Deviation Theory to the problem of structure growth on large-scale structure cosmology. Starting from gaussian distributed overdensities on concentric spherical shells, we show that a Large Deviation…
Number counts and redshift distribution of gravitational arcs are computed in the field of massive clusters of galaxies to probe the universe at high redshift. Using an accurate modelling for the cluster mass distribution and a model for…