Related papers: Isotropic Gaussian random fields on the sphere: Re…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
Approximation of elliptic PDEs with random diffusion coefficients typically requires a representation of the diffusion field in terms of a sequence $y=(y_j)_{j\geq 1}$ of scalar random variables. One may then apply high-dimensional…
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…
Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete…
We investigate graviton-photon oscillations sourced by cosmological magnetic fields from Gertsenshtein effect. We adopt a robust perturbative approach and we find that the conversion probability from graviton to photon can be resonantly…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
We consider elliptic diffusion problems with a random anisotropic diffusion coefficient, where, in a notable direction given by a random vector field, the diffusion strength differs from the diffusion strength perpendicular to this notable…
We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as…
Isotropic cosmology built in the Riemann-Cartan spacetime is investigated. Properties of homogeneous isotropic cosmological models filled with usual gravitating matter and scalar fields are studied in the beginning of cosmological expansion…
We develop and analyze a random field model for the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities provided by RANS simulations that is accessible to both a rigorous analytical validation…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
In this paper, aliasing effects are investigated for random fields defined on the d-dimensional sphere and reconstructed from discrete samples. First, we introduce the concept of an aliasing function on the sphere. The aliasing function…
We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent…
In this paper, we study the dynamical irregularity of the locally anisotropic spherical fluids in the context of Einstein-Gauss-Bonnet theory. We aim to describe the causes of energy-density irregularity of self-gravitating fluids and…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
Let $T$ be a random field invariant under the action of a compact group $G$. In the line of previous work we investigate properties of the Fourier coefficients as orthogonality and Gaussianity. In particular we give conditions ensuring that…
The Lorenz--Mie formulation of electromagnetic scattering by a homogeneous, isotropic, dielectric-magnetic sphere was extended to incorporate topologically insulating surface states characterized by a surface admittance $\gamma$.…
The link between Gaussian random fields and Markov random fields is well established based on a stochastic partial differential equation in Euclidean spaces, where the Mat\'ern covariance functions are essential. However, the Mat\'ern…
It has been shown that the large--scale correlation functions of the density field (and velocity divergence field) follow a specific hierarchy in the quasilinear regime and for Gaussian initial conditions (Bernardeau 1992). The exact…
We study the local times of a large class of Gaussian random fields satisfying strong local nondeterminism with respect to an anisotropic metric. We establish moment estimates and H\"{o}lder conditions for the local times of the Gaussian…