Related papers: The relationship between extremum statistics and u…
The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF),…
In quantum mechanics, the probability distribution function (PDF) and full counting statistics (FCS) play a fundamental role in characterizing the fluctuations of quantum observables, as they encode the complete information about these…
The statistical properties of the $E \times B$ flux in different types of plasma turbulence simulations are investigated using probability density distribution functions (PDF). The physics included in the models ranges from two dimensional…
The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…
We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution…
(Abridged) We discuss the probability distribution function (PDF) of column density resulting from density fields with lognormal PDFs, applicable to isothermal gas (e.g., probably molecular clouds). We suggest that a ``decorrelation…
Employing molecular dynamics simulations of jammed soft particles, we study microscopic responses of force-chain networks to quasi-static isotropic (de)compressions. We show that not only contacts but also interparticle gaps between the…
In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be…
We discuss the generation and statistics of the density fluctuations in highly compressible polytropic turbulence, based on a simple model and one-dimensional numerical simulations. Observing that density structures tend to form in a…
The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…
We propose a new, physically motivated fitting function for density PDFs in turbulent gas. Although it is known that when gas is isothermal, the PDF is approximately lognormal in the core, high-resolution simulations show large deviations…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…
We derive an analytical theory of the PDF of density fluctuations in supersonic turbulence in the presence of gravity in star-forming clouds. The theory is based on a rigorous derivation of a combination of the Navier-Stokes continuity…
Perturbation Theory (PT) applied to a cosmological density field with Gaussian initial fluctuations suggests a specific hierarchy for the correlation functions when the variance is small. In particular quantitative predictions have been…
We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian Processes (GPs) are used to model the PDF prior, while Bayes theorem…
We study the probability distribution $P$ of the sum of a large number of non-identically distributed random variables $n_m$. Condensation of fluctuations, the phenomenon whereby one of such variables provides a macroscopic contribution to…
We develop a diagrammatic technique to represent the multi-point cumulative probability density function (CPDF) of mass fluctuations in terms of the statistical properties of individual collapsed objects and relate this to other statistical…
This paper proposes a comprehensive and unprecedented framework that streamlines the derivation of exact, compact -- yet tractable -- solutions for the probability density function (PDF) and cumulative distribution function (CDF) of the sum…
Despite a long history and a clear overall understanding of properties of random walks on an incipient infinite cluster in percolation, some important information on it seems to be missing in the literature. In the present work, we revisit…
We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory…