Related papers: Generation of Arbitrarily Non-Gaussian Fields with…
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…
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…
We present a public code to generate random fields with an arbitrary probability distribution function (PDF) and an arbitrary correlation function. The algorithm is cosmology-independent, applicable to any stationary stochastic process over…
I present here a generalization of the maximum likelihood method and the $\chi^2$ method to the cases in which the data are {\it not} assumed to be Gaussian distributed. The method, based on the multivariate Edgeworth expansion, can find…
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…
In this paper we will consider the problem of the numerical simulation of non-Gaussian, scalar random fields with a prescribed correlation structure provided either by a theoretical model or computed on a set of observational data.…
We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
This document describes analytical and numerical techniques for the generation of Gaussian density fields, which represent cosmological density perturbations. The mathematical techniques involved in the generation of density harmonics in…
We present a generic algorithm for generating Gaussian random initial conditions for cosmological simulations on periodic rectangular lattices. We show that imposing periodic boundary conditions on the real-space correlator and choosing…
Gravitational lensing allows to quantify the angular distribution of the convergence field around clusters of galaxies to constrain their connectivity to the cosmic web. We describe in this paper the corresponding theory in Lagrangian space…
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
In this paper, we show how the structure of the landscape potential of the primordial Universe may be probed through the properties of the primordial density perturbations responsible for the origin of the cosmic microwave background…
Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of significant non-Gaussianity would thus have profound implications for…
We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many…
Analytic expressions for the statistics of peaks of random fields with weak non-Gaussianity are provided. Specifically, the abundance and spatial correlation of peaks are represented by formulas which can be evaluated only by virtually…
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 present a new tool for relating theory and experiment suited for non-Gaussian theories: non-Gaussian spectra. It does for non-Gaussian theories what the angular power spectrum $C_\ell$ does for Gaussian theories. We then show how…
We propose two methods for generating non-Gaussian maps with fixed power spectrum and bispectrum. The first makes use of a recently proposed rigorous, non-perturbative, Bayesian framework for generating non-Gaussian distributions. The…