Related papers: Gaussian Random Particles with Flexible Hausdorff …
Random fields in nature often have, to a good approximation, Gaussian characteristics. For such fields, the relative densities of umbilical points -- topological defects which can be classified into three types -- have certain fixed values.…
The present work investigates some exact solutions of the gravitational wave equation in some widely used cosmological spacetimes. The examples are taken from spatially flat and closed isotropic models as well as Kasner metric which is…
The quantum models of a massive scalar particle inside of an open bag generated by a pseudo-Gaussian conformaly flat (1+1) metrics are investigated. The potential of a free moving test particle, in the generated metric, has Gaussian…
The interaction between refraction from a distribution of inhomogeneous plasma and gravitational lensing introduces novel effects to the paths of light rays passing by a massive object. The plasma contributes additional terms to the…
This work aims to extend the existing results on thick points of logarithmic-correlated Gaussian Free Fields to Gaussian random fields that are more singular. To be specific, we adopt a sphere averaging regularization to study…
Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger (J. Chem. Phys. 65, 3968 (1976)), behaves like a weakly correlated ``mean field fluid'' over a…
In dimension 2 and above, the Burgers dynamics, the so-called "adhesion model" in cosmology, can actually give rise to several dynamics in the inviscid limit. We investigate here the statistical properties of the density field when it is…
The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field…
In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical…
We derive upper bounds on the Wasserstein distance ($W_1$), with respect to $\sup$-norm, between any continuous $\mathbb{R}^d$ valued random field indexed by the $n$-sphere and the Gaussian, based on Stein's method. We develop a novel…
We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account…
The likelihood function is a crucial element of parameter estimation. In analyses of galaxy overdensities and weak lensing shear, one often approximates the likelihood of the power spectrum with a Gaussian distribution. The posterior…
What particle shape will generate the highest packing fraction when randomly poured into a container? In order to explore and navigate the enormous search space efficiently, we pair molecular dynamics simulations with artificial evolution.…
The concept of geometric phase was applied to initiate the geometric-phase portrayal of electromagnetic scattering by a three-dimensional object in free space. Whereas the incident electromagnetic field is that of an arbitrarily polarized…
We investigated the equilibrium properties of a one-dimensional system of classical particles which interact in pairs through a bounded repulsive potential with a Gaussian shape. Notwithstanding the absence of a proper fluid-solid phase…
We study the imprints of massive particles with spin on cosmological correlators. Using the framework of the effective field theory of inflation, we classify the couplings of these particles to the Goldstone boson of broken time…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
The three-dimensional Gaussian beam transmission through a ferrite-semiconductor finely-stratified structure being under an action of an external static magnetic field in the Faraday geometry is considered. The beam field is represented by…
The angular two-point correlation function between background QSOs and foreground galaxies induced by gravitational lensing is derived. It is shown that the shape of this correlation function depends sensitively on the spectrum of the…