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We investigate the statistics of the mean magnetisation, of its large deviations and persistent large deviations in simple coarsening systems. We consider more specifically the case of the diffusion equation, of the Ising chain at zero…
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…
If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…
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…
In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter $y$. The performance parameter $y$ is random due to the presence of various sources…
The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded…
Parameter estimation in HEP experiments often involves Monte-Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization…
We derive a fully analytical, one-line closed-form expression for the cumulative distribution function (CDF) of the product of two correlated zero-mean normal random variables, avoiding any series representation. This result complements the…
Paper [1] derived the probability density function (PDF) of a sum of products of two correlated complex Gaussian zero-mean random variables (RVs) that has been applied to calculate the error probabilities of a \emph{M}-ary phase shift…
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
We discuss the product of $M$ rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint…
We examine the state of statistical equilibrium attained by a uniformly forced condensable substance subjected to advection in a periodic domain. In particular, we examine the probability density function (\pdf{}) of the condensable…
An x-ray scattering approach to determine the two-dimensional (2D) pair distribution function (PDF) in partially ordered 2D systems is proposed. We derive relations between the structure factor and PDF that enable quantitative studies of…
We present an analytical model for density-split correlation functions, that probe galaxy clustering in different density environments. Specifically, we focus on the cross-correlation between density-split regions and the tracer density…
We consider the statistics for the vorticity field in two-dimensional homogeneous isotropic turbulence (HIT). First, we exploit the invariance properties to derive dimensionally reduced governing equations for the one-point and two-point…
We consider two random variables $X$ and $Y$ following correlated Gamma distributions, characterized by identical scale and shape parameters and a linear correlation coefficient $\rho$. Our focus is on the parameter: \[ D(X,Y) = \frac{|X -…
We present a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. The PDF is represented as a path integral and is evaluated using the saddle-point method. It…
We discuss the positivity of parton distribution functions using the common $\overline{MS}$ factorization scheme. We find that in the perturbative regime $\overline{MS}$ PDFs inherit the strict positivity of physical PDFs. We explicitly…
The spin 1/2 XXZ chain in a random magnetic field pointing in the Z direction is numerically studied using the Density Matrix Renormalization Group (DMRG) method. The phase diagram as a function of the anisotropy of the XXZ Hamiltonian and…
We present a public code to generate random fields with an arbitrary probability distribution function (PDF) and an arbitrary correlation function. The algorithm is cosmology-independent, applicable to any stationary stochastic process over…