Related papers: The Affine Wigner Distribution
We revisit the problem of testing for multivariate reflected symmetry about an unspecified point. Although this testing problem is invariant with respect to full-rank affine transformations, among the hitherto few proposed tests only the…
We present a relativistic generalization of the Wigner inequality for the scalar and pseudoscalar particles decaying to two particles with spin (fermions and photons.) We consider Wigner's inequality with the full spin anticorrelation (with…
We study the deformation quantization of scalar and abelian gauge classical free fields. Stratonovich-Weyl quantizer, star-products and Wigner functionals are obtained in field and oscillator variables. Abelian gauge theory is particularly…
A theory of joint nonideal measurement of incompatible observables is used in order to assess the relative merits of quantum tomography and certain measurements of generalized observables, with respect to completeness of the obtained…
We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
We introduce kernel estimators for the semicircle law. In this first part of our general theory on the estimators, we prove the consistency and conduct simulation study to show the performance of the estimators. We also point out that…
The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear…
Message passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily graphical large models. The notion of a factor graph fragment allows for compartmentalization of algebra and…
The analysis of wave-packet dynamics may be greatly simplified when viewed in phase-space. While harmonic oscillators are often used as a convenient platform to study wave-packets, arbitrary state preparation in these systems is more…
In this note we exhibit recent advances in signal analysis via time-frequency distributions. New members of the Cohen class, generalizing the Wigner distribution, reveal to be effective in damping artefacts of some signals. We will survey…
We extend the random characteristics approach to Wigner matrices whose entries are not required to have a normal distribution. As an application, we give a simple and fully dynamical proof of the weak local semicircle law in the bulk.
We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schr\"odinger equations with bounded perturbations. To reach this goal, we perform a so-called $\mathcal{A}$-Wigner analysis…
Let $G$ be a finite group acting on $\mathbb{C}^N$. We study the problem of identifyng the class in $\mathbb{C}^N / G$ of a given signal: this encompasses several types of problems in signal processing. Some instances include certain…
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…
We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent…
The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…
The role of Wigner's little group, as an abelian gauge generator in different contexts, is studied.
Eigenvalue distributions of properly regularized Wilson loop operators are used to study the transition from ultra-violet (UV) behavior to infra-red (IR) behavior in gauge theories coupled to matter that potentially have an IR fixed point…
In this paper we study certain homogeneous spaces, which we call generalised affine Stiefel algebraic varieties. The main aim is to characterise the canonical divisor of generalised affine Stiefel algebraic varieties in terms of group…