Related papers: Mutual space-frequency distribution of Gaussian si…
Wigner distribution function has much importance in quantum statistical mechanics. It finds applications in various disciplines of physics including condense matter, quantum optics, to name but a few. Wigner distribution function is…
We consider Gaussian signals, i.e. random functions $u(t)$ ($t/L \in [0,1]$) with independent Gaussian Fourier modes of variance $\sim 1/q^{\alpha}$, and compute their statistical properties in small windows $[x, x+\delta]$. We determine…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…
This paper investigates the problem of Gaussian approximation for the wireless multi-access interference distribution in large spatial wireless networks. First, a principled methodology is presented to establish rates of convergence of the…
We apply a promising new method from the field of representations of Lie groups to calculate integrals over unitary groups, which are important for multi-antenna communications. To demonstrate the power and simplicity of this technique, we…
We demonstrate experimentally a novel technique for characterizing transverse spatial coherence using the Wigner distribution function. The presented method is based on measuring interference between a pair of rotated and displaced replicas…
Calculation of the distribution of the average value of a Gaussian random field in a finite domain is carried out for different cases. The results of the calculation demonstrate a strong dependence of the width of the distribution on the…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
This paper is concerned with the study of a circular random distribution called geodesic Normal distribution recently proposed for general manifolds. This distribution, parameterized by two real numbers associated to some specific location…
Two-frequency radiative transfer (2f-RT) theory is developed for geometrical optics in random media. The space-frequency correlation is described by the two-frequency Wigner distribution (2f-WD) which satisfies a closed form equation, the…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
The mutual information of two random variables i and j with joint probabilities t_ij is commonly used in learning Bayesian nets as well as in many other fields. The chances t_ij are usually estimated by the empirical sampling frequency…
Analytic expressions of the spatial coherence of partially coherent fields propagating in the Fresnel regime in all but the simplest of scenarios are largely lacking and calculation of the Fresnel transform typically entails tedious…
In the beginning of the 1950's, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum…
Consider an $N\times N$ hermitian random matrix with independent entries, not necessarily Gaussian, a so called Wigner matrix. It has been conjectured that the local spacing distribution, i.e. the distribution of the distance between…
In this paper we address a fundamental question in communication, that is, in the presence of various noise scenarios such as white/colored Gaussian noise and impulsive -type noises, how to efficiently and accurately transmit a set of…
We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral…