Related papers: Coordinates changed random fields on the sphere
We provide a method for fast and exact simulation of Gaussian random fields on spheres having isotropic covariance functions. The method proposed is then extended to Gaussian random fields defined over spheres cross time and having…
In Puplinskaite and Surgailis (2014) we introduced the notion of scaling transition for stationary random fields $X$ on $\mathbb{Z}^2$ in terms of partial sums limits, or scaling limits, of $X$ over rectangles whose sides grow at possibly…
Within the scope of a spherically symmetric space-time we study the role of different types of matter in the formation of different configurations with spherical symmetries. Here we have considered matter with barotropic equation of state,…
The motion of a local source inducing small oscillations in the gravitational field is investigated and shown to exhibit pure rotational kinetic energy. Should the net affect of these slow, revolving oscillations cause large-scale rotations…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
We show by using the method of matched asymptotic expansions that a sufficient condition can be derived which determines when a local experiment will detect the cosmological variation of a scalar field which is driving the spacetime…
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…
We study the transition between Zeeman levels of an arbitrary spin placed into a regular time-dependent field and a random field with the Gaussian distribution. One component of the regular field changes its sign at some moment of time,…
We introduce the spherical field formalism for free gauge fields. We discuss the structure of the spherical Hamiltonian for both general covariant gauge and radial gauge and point out several new features not present in the scalar field…
We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic…
We survey a decade worth of work pertaining to the nodal structures of random fields, with emphasis on the transformative techniques that shaped the field.
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…
We extend the "gauge choice" problem Lamb noticed to include a time-dependent relativistic non-perturbative Coulomb field, which can be produced by a cluster of relativistic charged particles. If adiabatic conditions are carefully…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
In this paper we define (empirical) quadratic variations for a Gaussian isotropic random field $f$ on a unit sphere as sums over equidistant increments on one single geodesic line on the surface of the sphere. We prove a noncentral limit…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…
Here, we analyze the primordial magnetic field transition between a radiative and a matter-dominated universe. The gravitational structure formation affects its evolution and energy spectrum. The structure excitation can trigger magnetic…
We present a useful method for the construction of cosmological models by solving the differential equations arising from calculating the kinematical invariants (shear, rotation, expansion and acceleration) of an observer field in proper…
Progress in astronomy comes from interpreting the signals encoded in the light received from distant objects: the distribution of light over the sky (images), over photon wavelength (spectrum), over polarization angle, and over time…