Related papers: Ergodicity and Gaussianity for Spherical Random Fi…
We review recent results concerning the spherically symmetric Einstein-scalar field system with positive cosmological constant. We do so by comparing with the classical results of Christodoulou concerning the asymptotically flat case…
We study the asymptotic behaviour of the nodal length of random $2d$-spherical harmonics $f_{\ell}$ of high degree $\ell \rightarrow\infty$, i.e. the length of their zero set $f_{\ell}^{-1}(0)$. It is found that the nodal lengths are…
In Euclidean space, the asymptotic shape of large cells in various types of Poisson driven random tessellations has been the subject of a famous conjecture due to David Kendall. Since shape is a geometric concept and large cells are…
We develop a powerful analytical formalism for calculating the energy density of the stochastic gravitational wave background, including a full description of its anisotropies. This is completely general, and can be applied to any…
The standard cosmological model predicts statistically isotropic cosmic microwave background (CMB) fluctuations characterized by the CMB temperature coefficients $a_{\ell m}$ being independent Gaussian random variables with zero mean and…
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…
Let ${\mathfrak{G}}\subset\mathbb{R}^{3}$ with $vol(\mathfrak{G})\sim L^{3}$. Let ${\mathscr{T}}(x)$ be a Gaussian random field $\forall~x\in\mathfrak{G}$ with expectation $\mathbf{E}[{\mathscr{T}}(x)]=0$ and correlation…
In this paper, we firstly calibrate the Amati relation (the $E_{\rm p}-E_{\rm iso}$ correlation) of gamma ray bursts (GRBs) at low redshifts ($z<0.8$) via Gaussian process by using the type Ia supernovae samples from Pantheon+ under the…
Asteroseismology, i.e. the study of the internal structures of stars via their global oscillations, is a valuable tool to obtain stellar parameters such as mass, radius, surface gravity and mean density. These parameters can be obtained…
In this paper we investigate the asymptotic behavior of the cosmological model based on phantom scalar field on the ground of qualitative analysis of the system of the cosmological model's differential equations and show that as opposed to…
We present simulations of the Cosmic Microwave Background Radiation (CMBR) power spectrum for a class of mixed, non-Gaussian, primordial random fields. We assume a skew positive mixed model with adiabatic inflation perturbations plus…
In this paper we consider the convex hull of a spherically symmetric sample in $R^d$. Our main contributions are some new asymptotic results for the expectation of the number of vertices, number of facets, area and the volume of the convex…
This work develops the asymptotic properties (weak consistency and Gaussianity), in the high-frequency limit, of approximate maximum likelihood estimators for the spectral parameters of Gaussian and isotropic spherical random fields. The…
The direct detection of gravitational waves has provided new opportunities for studying the universe, but also new challenges, such as the detection and characterization of stochastic gravitational-wave backgrounds at different…
This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…
The Random Wave Conjecture of M. V. Berry is the heuristic that eigenfunctions of a classically chaotic system should behave like Gaussian random fields, in the large eigenvalue limit. In this work we collect some definitions and properties…
We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…
Extended sources of the stochastic gravitational backgrounds have been conventionally searched on the spherical harmonics bases. The analysis during the previous observing runs by the ground-based gravitational wave detectors, such LIGO and…
The stochastic gravitational-wave background (SGWB) produced by merging neutron stars exhibits a peak in the kHz band. In this paper, we develop a theoretical framework to exploit this distinctive feature through a Markov Chain Monte Carlo…
In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics…