Related papers: Isotropic Gaussian random fields on the sphere: Re…
We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless non-conformal matter fields in the Early Universe. To this end, we supplement the stress-energy tensor of these fields with…
We study the peak height distribution of certain non-stationary Gaussian random fields. The explicit peak height distribution of smooth, non-stationary Gaussian processes in 1D with general covariance is derived. The formula is determined…
Gaussian random field on general ultrametric space is introduced as a solution of pseudodifferential stochastic equation. Covariation of the introduced random field is computed with the help of wavelet analysis on ultrametric spaces. Notion…
The statistically independent Karhunen-Loeve modes of refractive indices with isotropic Kolmogorov spectrum of the covariance are calculated in a sphere of given radius, rendered as series of 3D Zernike functions. Many of the symmetry…
We study the stochastic heat equation driven by an additive infinite dimensional fractional Brownian noise on the unit sphere $\mathbb{S}^{2}$. The existence and uniqueness of its solution in certain Sobolev space is investigated and sample…
This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally…
We present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We…
We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials…
We are concerned with the fast simulation of random fields on closed surfaces in $\mathbb{R}^3$ which are generated by the (Whittle-) Mat\'ern class of covariance functions. To this end, we solve the underlying fractional stochastic partial…
Using a method of eigenfunction expansion, a stochastic equation is developed for the generalized Schr{\"o}dinger equation with random fluctuations. The wave field $ {\psi} $ is expanded in terms of eigenfunctions: $ {\psi} = \sum_{n} a_{n}…
The spatial averaging used for the splitting of the local scale factor on the homogeneous background and small inhomogeneous perturbation leads to a non-local relationship between locally and globally defined comoving curvature…
We study isotropic Gaussian random fields on the high-dimensional sphere with an added deterministic linear term, also known as mixed p-spin Hamiltonians with external field. We prove that if the external field is sufficiently strong, then…
All prior applications of Diffusing-Wave Spectroscopy (DWS) to aqueous foams rely upon the assumption that the electric field of the detected light is a Gaussian random variable and that, hence, the Siegert relation applies. Here we test…
Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a random field in terms of its second order statistics, e.g.,…
We show that the anisotropies of the astrophysical stochastic gravitational wave background in the mHz band have a strong dependence on the modelling of galactic and sub-galactic physics. We explore a wide range of self-consistent…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem…
In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for…
Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations…
This paper presents a general form of the covariance matrix structure for a vector random field that is axially symmetric and mean square continuous on the sphere and provides a series representation for a longitudinally reversible one. The…