Related papers: Cosmic Statistics of Statistics
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
This paper focuses on two aspects of the statistics of cosmological observables that are important for the next stages of precision cosmology. First, we note that the theory of reduced angular $N$-point spectra has only been developed in…
We compute the shift in the epoch of matter-radiation equality due to the possible existence of a different statistical (non-extensive) background. The shift is mainly caused by a different neutrino-photon temperature ratio. We then…
A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to…
Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions…
We compute the exact asymptotics for the cumulants of linear statistics associated with the zeros counting measure of a large class of real Gaussian processes. Precisely, we show that if the underlying covariance function is regular and…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…
The spatial distribution of galaxies is a highly complex phenomenon currently impossible to predict deterministically. However, by using a statistical $\textit{bias}$ relation, it becomes possible to robustly model the average abundance of…
Star clusters are studied widely both as benchmarks for stellar evolution models and in their own right. Cluster age and mass distributions within galaxies are probes of star formation histories, and of cluster formation and disruption…
Fractional cosmology modifies the standard derivative to Caputo's fractional derivative of order $\mu$, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on $\mu$…
The cosmic large scale structure encodes the formation and evolution of a weblike network of dark matter and galaxies within the Universe. The cosmological information is wrapped up in non-Gaussian statistics requiring characterisation…
A new class of geometric statistics for analyzing galaxy catalogs is presented. {\it Filament statistics} quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are…
When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…
A new class of geometric statistics for analyzing galaxy catalogs is presented. Filament statistics quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are based…
The abundance and mass distribution of galaxy clusters is a sensitive probe of cosmological parameters, through the sensitivity of the high-mass end of the halo mass function to $\Omega_m$ and $\sigma_8$. While galaxy cluster surveys have…
We present the clustering of galaxy clusters as a useful addition to the common set of cosmological observables. The clustering of clusters probes the large-scale structure of the Universe, extending galaxy clustering analysis to the…
The complexity and accuracy of current and future precision cosmology observational campaigns has made it essential to develop an efficient technique for directly combining simulation and observational datasets to determine cosmological and…
The Cosmic Defect theory has been confronted with four observational constraints: primordial nuclear species abundances emerging from the big bang nucleosynthesis; large scale structure formation in the universe; cosmic microwave background…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…