Related papers: Cosmic Statistics of Statistics
The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear…
Ongoing and future wide-field galaxy surveys can be used to locate a number of clusters of galaxies with cosmic shear measurement alone. We study constraints on cosmological models using statistics of weak lensing selected galaxy clusters.…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
In this thesis, we discuss some of the applications of cosmological perturbation theory in the late universe. We begin by reviewing the tools used to understand the standard model of cosmology theoretically and to compute its observational…
The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, Mosimann (1963) derived general formulas for the falling…
We propose to use a simple observable, the fractional area of "hot spots" in weak gravitational lensing mass maps which are detected with high significance, to determine background cosmological parameters. Because these high-convergence…
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…
Weak lensing of galaxies and CMB photons through the large-scale structure of the Universe is one of the most promising cosmological probes with upcoming experiments dedicated to its measurements such as Euclid/LSST and CMB Stage 4…
The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…
We present analytic formulae for the integral number count distribution of cosmological bursting or steady sources valid over the entire range of fluxes, including density evolution and either standard candle or a power law luminosity…
In Papers I-III [arXiv:2210.10435, arXiv:2210.11085, arXiv:2304.13304], we use the flat-sky and distant-observer approximations to develop a formalism with which the correlation statistics of cosmological tensor fields are calculated by the…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
The Universe's assumed homogeneity and isotropy is known as the cosmological principle. It is one of the assumptions that lead to the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metric and it is a cornerstone of modern cosmology,…
We obtain a power saving in the error term for a semigroup congruence lattice point count related to continued fractions. This is done by adapting arguments from recent work of Oh and Winter (2014) that give uniform bounds for certain…
To understand their data better, astronomers need to use statistical tools that are more advanced than traditional ``freshman lab'' statistics. As an illustration, the problem of combining apparently incompatible measurements of a quantity…
I critically review a methodology of using clusters of galaxies as cosmological probes. The understanding of the abundances and spatial correlations of dark matter halos has been significantly advanced especially for a last few years.…
Based on thermodynamics, we study the galactic clustering of an expanding Universe by considering the logarithmic and volume (quantum) corrections to Newton's law along with the repulsive effect of a harmonic force induced by the…
This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various…
For arbitrary $\beta > 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $\beta$ ensembles. We identify the distribution of these…
Galaxy clusters are one of the most powerful probes to study extensions of General Relativity and the Standard Cosmological Model. Upcoming surveys like the Vera Rubin Observatory's Legacy Survey of Space and Time are expected to…