Related papers: Cumulants as non-Gaussian qualifiers
It is shown that under essentially all conditions, the non-linear classical equations governing gravitation and matter in cosmology have a solution in which far outside the horizon in a suitable gauge the reduced spatial metric (the spatial…
The redshift dependence of the abundance of galaxy clusters is very sensitive to the statistical properties of primordial density perturbations. It can thus be used to probe small deviations from Gaussian initial conditions. Such deviations…
We compare the latest results from CMB experiments at scales around $l_e \sim 150$ over different parts of the sky to test the hypothesis that they are drawn from a Gaussian distribution, as is usually assumed. Using both the diagonal and…
We introduce a family of criteria to detect quantum non-Gaussian states of a harmonic oscillator, that is, quantum states that can not be expressed as a convex mixture of Gaussian states. In particular we prove that, for convex mixtures of…
Accounting for all the relativistic effects, we have developed the fully nonlinear gauge-invariant formalism for describing the cosmological observables and presented the second-order perturbative expressions associated with light…
We establish the convergence of the densities of a sequence of nonlinear functionals of an underlying Gaussian process to the density of a Gamma distribution. The key idea of our work is a new density formula for random variables in the…
A convincing detection of primordial non-Gaussianity in the cosmic background radiation (CMB) is essential to probe the physics of the early universe. Since a single statistical estimator can hardly be suitable to detect the various…
Central moments and cumulants are often employed to characterize the distribution of data. The skewness and kurtosis are particularly useful for the detection of outliers, the assessment of departures from normally distributed data,…
We study the behavior of n-point functions of the primordial curvature perturbations, assuming our observed Universe is only a subset of a larger space with statistically homogeneous and isotropic perturbations. If the larger space has…
Gravitational lensing of the Cosmic Microwave Background (CMB) encodes cosmological information in the observed anisotropies of temperature and polarization. Accurate extraction of this additional information requires precise modeling of…
We obtain a general solution for the probability density function of wave intensities in non-stationary Wave Turbulence. The solution is expressed in terms of the wave action spectrum evolving according the the wave-kinetic equation. We…
An experimental study of current fluctuations through a tunable transmission barrier, a quantum point contact, are reported. We measure the probability distribution function of transmitted charge with precision sufficient to extract the…
We show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of $U$-statistics, built from wavelets coefficients evaluated on a homogeneous spherical Poisson field of arbitrary dimension.…
We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of…
Cosmic microwave background (CMB) temperature anisotropies follow a Gaussian statistical distribution in the standard inflationary model, but there are non-Gaussian contributions due to astrophysical foregrounds. The detection of the…
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…
The detection of primordial non-Gaussianity could provide a powerful means to test various inflationary scenarios. Although scale-invariant non-Gaussianity (often described by the $f_{NL}$ formalism) is currently best constrained by the…
An alternative parametric description for discrete random variables, called muculants, is proposed. In contrast to cumulants, muculants are based on the Fourier series expansion, rather than on the Taylor series expansion, of the logarithm…
Several cosmological measurements have attained significant levels of maturity and accuracy over the last decade. Continuing this trend, future observations promise measurements of the statistics of the cosmic mass distribution at an…
A very important property of a statistical distribution is to know whether it obeys Gaussian statistics or not. On the one hand, it is of paramount importance in the context of CMB anisotropy studies, since deviations from a Gaussian…