We discuss the requirements of good statistics for quantifying nonGaussianity in the Cosmic Microwave Background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes incompatible. It is shown that the first of these requirements prefers a real space (or wavelet) formulation, whereas the latter favours quantities defined in Fouri...

the mean and variance of the lagrangian katz family of distribution (lkd), the basiclagrangian katz distribution of type i (lkd-i) and type ii (lkd-ii) are provided in an easy method.the recurrence relation between the non-central, central and factorial moments, and the recurrencerelation between moments and cumulants of lkd, lkd-i and lkd-ii are given. the first fourcumulants of lkd-i and lkd-...

In non-commutative probability theory, cumulants and their appropriate generating function are defined when a notion of independence is given [17, 18, 19]. They are useful especially in the central limit theorem and Poisson’s law of small numbers. We denote by any one of classical, free and boolean convolutions. We denote by Dλ the dilation operator defined by (Dλμ)(B) = μ(λ B) for any Borel se...

Recently, it has been shown that the ground-state energy of a quantum many-body system can be written in terms of cumulants. In this paper we show that the energies of excited states can be expressed similarly. These representations are suitable for various approximation schemes, e.g., projection techniques. The explicit use of cumulants ensures size consistency in all approximations. The theor...

The current trend in the statistical analysis of chaos shows certain gaps particularly regarding the engineering applications. This paper, which is a sequel of previous publications from the authors [1-5], develops an application of the cumulant approach to the analysis of the covariance properties of chaotic signals. A general approach for the analysis of two-moment cumulants is considered, pa...

We investigate the probability distribution that governs the number of ground-state particles in a partially condensed ideal Bose gas confined to a cubic volume within the canonical ensemble. Imposing either periodic or Dirichlet boundary conditions, we derive asymptotic expressions for all its cumulants. Whereas the condensation temperature becomes independent of the boundary conditions in the...

We present a comprehensive theoretical analysis of the dc transport properties of superconducting point contacts. We determine the full-counting statistics for these junctions, which allows us to calculate not only the current or the noise, but all the cumulants of the current distribution. We show how the knowledge of the statistics of charge transfer provides an unprecedented level of underst...

We present a method based on three-particle azimuthal correlation cumulants for the study of the interaction of jets with the medium produced in heavy ion collisions at RHIC and LHC where jets cannot be reconstructed on an event-by-event basis with conventional jet finding algorithms. The method is specifically designed to distinguish a range of jet interaction mechanisms such as Mach cone emis...