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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…
Study of parton distribution functions (PDFs) has led to a finer cognisance of the structure of partons in hadrons and the proton structure functions in deep inelastic scattering (DIS). PDFs are instrumental in predicting results for most…
A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…
The probability density function (PDF) of the logarithmic density contrast, $s=\ln (\rho/\rho_0)$, with gas density $\rho$ and mean density $\rho_0$, for hydrodynamical supersonic turbulence is well-known to have significant non-Gaussian…
Accurately measuring magnetic field strength in the interstellar medium, including giant molecular clouds (GMCs), remains a significant challenge. We present a machine learning approach using Denoising Diffusion Probabilistic Models (DDPMs)…
In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…
We study the effects of radiative transfer on the Probability Distribution Functions (PDFs) of simulations of magnetohydrodynamic turbulence in the widely studied $^{13}$CO 2-1 transition. We find that the integrated intensity maps…
Perturbative quantum chromodynamics (QCD) ceases to be applicable at low interaction energies due to the rapid increase of the strong coupling. In that limit, the non-perturbative regime determines the properties of quarks and gluons…
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This…
Photon counts statistics have recently been proven to provide a sensitive observable for characterizing gamma-ray source populations and for measuring the composition of the gamma-ray sky. In this work, we generalize the use of the standard…
We present a general framework to treat the evolution of one-point probability distribution function (PDF) for cosmic density $\delta$ and velocity-divergence fields $\theta$. In particular, we derive an evolution equation for the one-point…
Accurate Standard Model predictions of proton-proton collisions are essential for interpreting the current and forthcoming experimental measurements from high-energy colliders. The quest for physics beyond the Standard Model is in fact…
Neutrino Deep Inelastic Scattering on nuclei is an essential process to constrain the strange quark parton distribution functions in the proton. The critical component on the way to using the neutrino DIS data in a proton PDF analysis is…
In a search for the signature of turbulence in the diffuse interstellar medium in gas density distributions, we determined the probability distribution functions (PDFs) of the average volume densities of the diffuse gas. The densities were…
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…
At any given scale, 3$\times$2-point statistics extract only three numbers from the joint distribution of the cosmic matter density and galaxy density fluctuations: their variances and their covariance. It is well known that the full shape…
We revisit the mass-size relation of molecular cloud structures based on the column density map of the Cygnus-X molecular cloud complex. We extract 135 column density peaks in Cygnus-X and analyze the column density distributions around…
Numerical simulations of magneto-convection and analysis of solar magnetogram data provide empirical probability density functions (PDFs) for the line-of-sight component of the magnetic field. In this paper, we theoretically explore effects…
Turbulence is essential for understanding the structure and dynamics of molecular clouds and star-forming regions. There is a need for adequate tools to describe and characterize the properties of turbulent flows. One-point probability…
We compute the one-point PDF of an initially Gaussian dark matter density field using spherical collapse (SC). We compare the results to other forms available in the literature and also compare the PDFs in the $\Lambda$CDM model with an…