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We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or…
We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the $p$-order hierarchical amplitudes $S_p$, in both real and redshift space. We…
Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data…
We study the probability distribution function (PDF) of the mass density in simulations of supersonic turbulence with properties appropriate for molecular clouds. For this study we use Athena, a new higher-order Godunov code. We find there…
The log-normal distribution represents the probability of finding randomly distributed particles in a micro canonical ensemble with high entropy. To a first approximation, a modified form of this distribution with a truncated termination…
The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
Statistical analyses of finite sample distributions usually assume that fluctuations are self-averaging, i.e. that they are statistically similar in different regions of the given sample volume. By using the scale-length method, we test…
We study the one-point probability distribution function (PDF) for matter density averaged over spherical cells. The leading part to the PDF is defined by spherical collapse dynamics, whereas the next-to-leading part comes from the…
In this paper I show how the statistics of the gravitational field is changed when the system is characterized by a non-uniform distribution of particles. I show how the distribution functions W(dF/dt) giving the joint probability that a…
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…
This paper deals with a new class of random flights $\underline{\bf X}_d(t),t>0,$ defined in the real space $\mathbb{R}^d, d\geq 2,$ characterized by non-uniform probability distributions on the multidimensional sphere. These random motions…
The evolution of probability distribution functions (PDFs) of continuous density, velocity and velocity derivatives ( deformation tensor) fields in the theory of cosmological gravitational instability are considered. We show that in the…
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the…
We conduct numerical experiments to determine the density probability distribution function (PDF) produced in supersonic, isothermal, self-gravitating turbulence of the sort that is ubiquitous in star-forming molecular clouds. Our…
It is the common lore to assume that knowing the equation for the probability distribution function (PDF) of a stochastic model as a function of time tells the whole picture defining all other characteristics of the model. We show that this…
We present the first prediction of the probability distribution function (PDF) for self-organization of shear flows modeled by a nonlinear diffusion equation with a stochastic forcing. A novel non-perturbative method based on a coherent…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…
We present a first principle approach to obtain analytical predictions for spherically-averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation…
Ambiguity sets of probability distributions are used to hedge against uncertainty about the true probabilities of random quantities of interest (QoIs). When available, these ambiguity sets are constructed from both data (collected at the…