Related papers: Numerical Simulation of Non-Gaussian Random Fields…
We provide theoretical procedures and practical recipes to simulate non-Gaussian correlated, homogeneous random fields with prescribed marginal distributions and cross-correlation structure, either in a N-dimensional Cartesian space or on…
Non-Gaussianity in the cosmic microwave background and the large-scale structure of galaxies provides an increasingly powerful probe of the universe. I implement an algorithm to generate realisations of fields that possess an arbitrary…
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…
This paper describes the generation of initial conditions for numerical simulations in cosmology with multiple levels of resolution, or multiscale simulations. We present the theory of adaptive mesh refinement of Gaussian random fields…
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…
Phenomenologically interesting scalar potentials are highly atypical in generic random landscapes. We develop the mathematical techniques to generate constrained random potentials, i.e. Slepian models, which can globally represent…
Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is…
Context. In previous work, we developed a quasi-Gaussian approximation for the likelihood of correlation functions, which, in contrast to the usual Gaussian approach, incorporates fundamental mathematical constraints on correlation…
The statistical translation invariance of cosmological random fields is broken by a finite survey boundary, correlating the observable Fourier modes. Standard methods for generating Gaussian fields either neglect these correlations, or are…
The presented paper is devoted to statistical modeling of Gaussian scalar real random fields inside a three-dimensional sphere (ball). We propose a statistical model describing the spatial heterogeneity in a unit ball and a numerical…
This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient…
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in…
Structure formation in our Universe creates non-Gaussian random fields that will soon be observed over almost the entire sky by the Euclid satellite, the Vera-Rubin observatory, and the Square Kilometre Array. An unsolved problem is how to…
Gaussian Schell-model fields are examples of spatially partially coherent fields, which in recent years have found several unique applications. The existing techniques for generating Gaussian Schell-model (GSM) fields are based on…
We provide a graphical method to describe and analyze non-Gaussian quantum states using a hypergraph framework. These states are pivotal resources for quantum computing, communication, and metrology, but their characterization is hindered…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
We formulate the statistics of peaks of non-Gaussian random fields and implement it to study the sphericity of peaks. For non-Gaussianity of the local type, we present a general formalism valid regardless of how large the deviation from…
A simple method is presented for the rapid simulation of statistically-isotropic non-Gaussian maps of CMB temperature fluctuations with a given power spectrum and analytically-calculable bispectrum and higher-order polyspectra. The…