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In this paper we examine the deviations from Gaussianity for two types of random variable converging to a normal distribution, namely sums of random variables generated by a deterministic discrete time map and a linearly damped variable…
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy…
We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are…
The transverse momentum per particle, $[p_t]$, fluctuates event by event in ultrarelativistic nucleus-nucleus collisions, for a given multiplicity. These fluctuations are small and approximately Gaussian, but a non-zero skewness has been…
We revisit effective scenarios for the origin of heavy tails in stationary velocity distributions. A first analysis combines localization with diffusive acceleration. That gets realized in space plasmas to find the so-called…
We investigate statistical distributions of differences in gravitational-lensing deflections between two light rays, the so-called lensing excursion angles. A probability distribution function of the lensing excursion angles, which plays a…
Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability…
Exponential, and not Gaussian, decay of probability density functions was studied by Laplace in the context of his analysis of errors. Such Laplace propagators for the diffusive motion of single particles in disordered media were recently…
Fluctuations due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes and duration times are considered. These are demonstrated to be strongly intermittent in the limit of weak pulse overlap,…
We investigate the evolution of the skewness of the distribution of density fluctuations in CDM models with both Gaussian and non--Gaussian initial fluctuations. We show that the method proposed by Coles \& Frenk (1991), which uses the…
On the grounds of both widely known experimental and numerical data of the strain-rate tensor statistical properties in the fully developed incompressible turbulent flow and the integral transformations deduced in the article, some…
Experiments involving the two-dimensional passive diffusion of colloidal boomerangs tracked off their centre of mobility have shown striking non-Gaussian tails in their probability distribution function [Chakrabarty et al., Soft Matter 12,…
Bouchet et al. (1992) showed that in an open or closed Universe with only pressureless matter, gravitational instability from Gaussian initial conditions induces a normalized skewness, $S_3 \equiv \VEV{\delta^3} \VEV{\delta^2}^{-2}$, that…
Pairwise velocities of the large-scale structure encode valuable information about the growth of structure. They can be observed indirectly through redshift-space distortions and the kinetic Sunyaev-Zeldovich effect. Whether it is Gaussian…
A random flight on a plane with non-isotropic displacements at the moments of direction changes is considered. In the case of exponentially distributed flight lengths a Gaussian limit theorem is proved for the position of a particle in the…
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…
The problem of sums of independent, identically distributed random variables with stretched-exponential tails exhibits a dynamical phase transition and has recently reemerged in the context of active transport and condensation phenomena. We…
High resolution numerical simulations of stationary inverse energy cascade in two-dimensional turbulence are presented. Deviations from Gaussianity of velocity differences statistics are quantitatively investigated. The level of statistical…
Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain-rate with highly non-Gaussian statistics.…
Long tails in the velocity distribution are observed in plasmas and gravitational systems. Some experiments and observations in far-from-equilibrium conditions show that these tails behave as 1/v^(5/2). We show here that such heavy tails…