Related papers: Polar sets of anisotropic Gaussian random fields

We study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII$_{0}$, VII$_{h}$ and…

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences…

It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random…

Let T be a random field invariant under the action of a compact group G We give conditions ensuring that independence of the random Fourier coefficients is equivalent to Gaussianity. As a consequence, in general it is not possible to…

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…

The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…

Let ($\Sigma$, g) be a closed connected surface equipped with a riemannian metric. Let ($\lambda$ n) n$\in$N and ($\psi$ n) n$\in$N be the increasing sequence of eigenvalues and the sequence of corresponding L 2-normalized eigenfunctions of…

We present several refinements on the fluctuations of sequences of random vectors (with values in the Euclidean space $\mathbb{R}^d$) which converge after normalization to a multidimensional Gaussian distribution. More precisely we refine…

In this paper, we characterize the asymptotic and large scale behavior of the eigenvalues of wavelet random matrices in high dimensions. We assume that possibly non-Gaussian, finite-variance $p$-variate measurements are made of a…

The Gaussian unitary random matrix ensembles satisfying some additional symmetry conditions are considered. The effect of these conditions on the limiting normalized counting measures and correlation functions is studied.

This paper extends previous work on echo chambers modeled by an Ising-like system at zero temperature (1. Echo Chambers and random Polarization, Symmetry 2024, 16(12), 1566). There, polarization emerged as a spontaneous symmetry-breaking…

In classical random matrix theory the Gaussian and chiral Gaussian random matrix models with a source are realized as shifted mean Gaussian, and chiral Gaussian, random matrices with real $(\beta = 1)$, complex ($\beta = 2)$ and real…

A modified version of a finite random field Ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making. Fields may have a non-zero average. A postulate of minimum…

We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…

Series expansions of isotropic Gaussian random fields on $\mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to…

We investigate the Gaussian small ball probabilities with random centers, find their deterministic a.s.-equivalents and establish a relation to infinite-dimensional high-resolution quantization.

In the EFT of biased tracers the noise field $\varepsilon_g$ is not exactly uncorrelated with the nonlinear matter field $\delta$. Its correlation with $\delta$ is effectively captured by adding stochasticities to each bias coefficient. We…

Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random…