Related papers: Models of space-time random fields on the sphere
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
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 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…
We study the out of equilibrium dynamics of an elastic manifold in a random potential using mean-field theory. We find two asymptotic time regimes: (i) stationary dynamics, (ii) slow aging dynamics with violation of equilibrium theorems. We…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
We establish spectral expansions of homogeneous and isotropic random fields taking values in the $3$-dimensional Euclidean space $E^3$ and in the space $\mathsf{S}^2(E^3)$ of symmetric rank $2$ tensors over $E^3$. The former is a model of…
Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…
We consider the correlation structure of the random coefficients for a wide class of wavelet systems on the sphere (Mexican needlets) which were recently introduced in the literature by Geller and Mayeli (2007). We provide necessary and…
Fluctuations in the large-scale structure of the Universe contain significant information about cosmological physics, but are modulated in survey datasets by various observational effects. Building on existing literature, we provide a…
Spatial and spatiotemporal volatility models are a class of models designed to capture spatial dependence in the volatility of spatial and spatiotemporal data. Spatial dependence in the volatility may arise due to spatial spillovers among…
We introduce a class of space-times modeling singular events such as evaporating black holes and topology changes, which we dub as semi-globally hyperbolic space-times. On these space-times we aim to study the existence of reasonable…
Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is…
We introduce a methodology to test models with spatial variations of the fine-structure constant $\alpha$, based on the calculation of the angular power spectrum of these measurements. This methodology enables comparisons of observations…
Phase-space descriptions are used to find qualitative features of the solutions of generalized scalar field cosmologies with arbitrary potentials and arbitrary couplings to matter. Previous results are summarized and new ones are presented…
We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…
We study scalar field and electromagnetic perturbations on Locally Rotationally Symmetric (LRS) class II spacetimes, exploiting a recently developed covariant and gauge-invariant perturbation formalism. From the Klein-Gordon equation and…
We search for time-dependent solutions for the 5-dimensional system of a scalar field canonically coupled to gravity. Time-independent and time-dependent scalar field configurations with the most general homogeneous and isotropic 4D metric…
Within the scope of a spherically symmetric space-time we study the role of a nonlinear spinor field in the formation of different configurations with spherical symmetries. The presence of the non-diagonal components of energy-momentum…
It is shown that, in the model of a flat 3D space, the time (i.e., the Hubble or the gravitation constant) plays a role of a spatial property. Gravitation field of spherical central mass does not lead to a lowering of symmetry of the space…
Based on the concept of curved spacetime in Einsteinian General Relativity, the field theories and their quantum theories in the curved octonion spaces etc are discussed. The research results discover the close relationships of the curved…