Related papers: Constructing PDFs of spatially dependent fields us…
The probability density function (PDF) of some global average quantity plays a fundamental role in critical and highly correlated systems. We explicitly compute this quantity as a function of the magnetization for the two dimensional XY…
PDFs can be studied directly using lattice QCD by evaluating matrix elements of non-local operators. A number of groups are pursuing numerical calculations and investigating possible systematic uncertainties. One systematic that has…
The purpose of the present paper is to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of the velocity field of a turbulent flow. The PDF PDE is a highly non-linear…
Based on the canonical correlation analysis we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
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…
Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is…
Container ships encounter large roll angles and high acceleration, and container loss remains a problem. This study proposes a method for calculating the probability density function~(PDF) of roll angular and cargo lateral accelerations.…
This paper investigates probability density functions (PDFs) that are continuous everywhere, nearly uniform around the mode of distribution, and adaptable to a variety of distribution shapes ranging from bell-shaped to rectangular. From the…
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 present SMPDF Web, a web interface for the construction of parton distribution functions (PDFs) with a minimal number of error sets needed to represent the PDF uncertainty of specific processes (SMPDF).
Representing the parton distribution functions (PDFs) of the proton and other hadrons through flexible, high-fidelity parametrizations has been a long-standing goal of particle physics phenomenology. This is particularly true since the…
This letter provides the first prediction of the probability density function (PDF) of flux $R$ in plasma sheath sheath region in magnetic fusion devices which is characterized by dynamical equations with exponential non-linearities. By…
We derive a first order linear differential equation describing the shape of the probability density function of magnetic field strengths in the quiet Sun (PDF). The modeling is very schematic. It considers convective motions which…
Parton distribution functions (PDFs) describe universal properties of bound states and allow us to calculate scattering amplitudes in processes with large momentum transfer. Calculating PDFs involves the evaluation of matrix elements with a…
We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation. The procedure involves obtaining an initial estimate of…
Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…