Related papers: Genus Statistics of the Large-Scale Structure with…
We investigate number count statistics as measures for transition to homogeneity of the matter distribution in the Universe and analyse how such statistics might be `dressed' by the assumed survey selection function. Since the estimated…
The growth rate of cosmic structure is a powerful cosmological probe for extracting information on the gravitational interactions and dark energy. In the late time Universe, the growth rate becomes non-linear and is usually probed by…
The distribution of matter in the universe is, to first order, lognormal. Improving this approximation requires characterization of the third moment (skewness) of the log density field. Thus, using Millennium Simulation phenomenology and…
Evolution and abundance of the large-scale structures we observe today, such as clusters of galaxies, is sensitive to the statistical properties of dark matter primordial density fluctuations, which is assumed to follow a Gaussian…
We study the effect of the non-Gaussian clustering of galaxies on the statistics of pencil beam surveys. We find that the higher order moments of the galaxy distribution play an important role in the probability distribution for the power…
For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…
Models of structure formation in the universe postulate that matter distributions observed today in galaxy catalogs arise, through a complex non-linear dynamics, by gravitational evolution from a very uniform initial state. Dark matter…
We develop technique concerning statistical analyses of the large-scale structure of the universe in the presence of biasing in the structure formation. We formulate the diagrammatic method to calculate the correlation functions of the…
The galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future Large Scale Structure surveys. The precision demanded by these Stage IV surveys requires the use of second…
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…
We analyze multi-field inflationary systems which yield strongly scale dependent non-Gaussianity with a shape that is very close to the local shape. As in usual multi-field models, the non-Gaussianity arises from the non-linear transfer of…
This paper theoretically analyzes a phenomenological stochastic model for bacterial growth. This model comprises cell division and the linear growth of cells, where growth rates and cell cycles are drawn from lognormal distributions. We…
High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG,…
For general non-Gaussian distributions, the covariance and precision matrices do not encode the independence structure of the variables, as they do for the multivariate Gaussian. This paper builds on previous work to show that for a class…
I present here a generalization of the maximum likelihood method and the $\chi^2$ method to the cases in which the data are {\it not} assumed to be Gaussian distributed. The method, based on the multivariate Edgeworth expansion, can find…
I investigate the use of Pearson's chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) for the determination of the goodness-of-fit between…
Clustering of large-scale structure provides significant cosmological information through the power spectrum of density perturbations. Additional information can be gained from higher-order statistics like the bispectrum, especially to…
We present in this paper a quantitative method for defining void size in large-scale structure based on percolation threshold density. Beginning with two-dimensional gravitational clustering simulations smoothed to the threshold of…
We have investigated a weighted chi-square distribution of the variable $\xi$ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles $\phi_k=2\pi k/N$, where $k \in \{0,1,...,N-1\}$…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…