Related papers: Two theorems on distribution of Gaussian quadratic…
Convex analysis and Gaussian probability are tightly connected, as mostly evident in the theory of linear regression. Our work introduces an algebraic perspective on such relationship, in the form of a diagrammatic calculus of string…
Quadratic variations of Gaussian processes play important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
This article proposes a new filtering model for stationary Gaussian Markov statistical experiments, given by diffusion-type difference stochastic equations.
The generalized Gaussian distribution that stems from information theory is studied. The log-Minkowski problem associated with generalized Gaussian distribution shall be introduced and solved.
We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).
In this paper, we establish a demi-distributions theory which develops the usual distribution theory, in particular, we show that many conclusions as differentiations, Fourier transforms and convolutions can be generalized to the…
Generalized parton distributions have been introduced in recent years as a suitable theoretical tool to study the structure of the nucleon. Unifying the concepts of parton distributions and hadronic form factors, they provide a…
Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.
A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…
An extension of the Gaussian correlation conjecture (GCC) is proved for multivariate gamma distributions (in the sense of Krishnamoorthy and Parthasarathy). The classical GCC for Gaussian probability measures is obtained by the special case…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
Erd\H{o}s and Hall studied the angular distribution of Gaussian integers with a fixed norm. We generalize their result to the angular distribution of integral ideal numbers with a fixed norm in any quadratic extension.
In this work, we explore both the ordinary $q$-Gaussian distribution and a new one defined here, determining both their mean and variance, and we use them to construct solutions of the $q$-deformed diffusion differential equation. This…
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…
Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations…
The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…
A two-dimensional Gauss-Kuzmin theorem for $N$-continued fraction expansions is shown. More exactly, we obtain a Gauss-Kuzmin theorem related to the natural extension of the measure-dynamical system corresponding to these expansions. Then,…
In this paper, we apply high level versions of Jacobi's derivative formula to number theory such as quarternary quadratic forms and convolution sums of some arithmetical functions.
Using ideas of Ramakrishnan, we consider the icosahedral analogue of the theorems of Sarnak and Brumley on Hecke-Maass newforms with Fourier coefficients in a quadratic order. Although we are unable to conclude the existence of an…