Related papers: Cumulants as non-Gaussian qualifiers
The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…
The trispectrum of the cosmic microwave background can be used to assess the level of non-Gaussianity on cosmological scales. It probes the fourth order moment, as a function of angular scale, of the probability distribution function of…
We compute the exact asymptotics for the cumulants of linear statistics associated with the zeros counting measure of a large class of real Gaussian processes. Precisely, we show that if the underlying covariance function is regular and…
We present a simple way to calculate non-Gaussianity in inflation using fully non-linear equations on long wavelengths with stochastic sources to take into account the short-wavelength quantum fluctuations. Our formalism includes both…
We study the non-Gaussian tail of the probability distribution function of density in cosmological N-Body simulations for a variety of initial conditions. We compare the behaviour of the non-Gaussian tail in the real space with that in the…
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…
Currently, it appears that the best method for non-Gaussianity detection in the Cosmic Microwave Background (CMB) consists in calculating the kurtosis of the wavelet coefficients. We know that wavelet-kurtosis outperforms other methods such…
In continuous variable optical platforms, large-scale Gaussian cluster states have already been demonstrated, but non-Gaussian resources are essential to achieve universality and fault tolerance in measurement-based quantum computation.…
We consider Gaussian quantum circuits supplemented with non-Gaussian input states and derive sufficient conditions for efficient classical strong simulation of these circuits. In particular, we generalise the stellar representation of…
In (Hansen et al. 2002) we presented a new approach for measuring non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern, based on the multivariate empirical distribution function of the spherical harmonics a_lm of a…
What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a…
We address the quantification of non-Gaussianity of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in details the properties and the relationships of two recently proposed…
The detection of non-Gaussianity in the CMB data would rule out a number of inflationary models. A null detection of non-Gaussianity, instead, would exclude alternative models for the early universe. Thus, a detection or non-detection of…
A nonsingular bouncing cosmology in which the scales of interest today exit the Hubble radius in a matter-dominated contracting phase yields an alternative to inflation for producing a scale-invariant spectrum of adiabatic cosmological…
Recent Cosmic Microwave Background (CMB) observations indicate that the temperature anisotropies arise from quantum fluctuations in the inflationary scenario. In the simplest inflationary models, the distribution of CMB temperature…
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…
We present the experimental investigation of the non-Gaussian nature of some mixtures of Fock states by reconstructing their Wigner function and exploiting two recently introduced measures of non-Gaussianity. In particular, we demonstrate…
We investigate the relative sensitivities of several tests for deviations from Gaussianity in the primordial distribution of density perturbations. We consider models for non-Gaussianity that mimic that which comes from inflation as well as…
It is possible to classify pixels of a smoothed cosmic microwave background (CMB) fluctuation map according to their local curvature in ``hill'', ``lake'' and ``saddle'' regions. In the Gaussian case, fractional areas occupied by pixels of…
Minkowski Functionals (MFs) are topological statistics that have become one of many standard tools used for investigating the statistical properties of cosmological random fields. They have found regular use in studies of departures from…