Related papers: Two theorems on distribution of Gaussian quadratic…
The paper deals with a generalisation of uniform distribution. The analogues of Weyl's criterion are derived.
I briefly discuss some recent developments (and recall some old news) in the theory and phenomenology of generalised parton distributions.
Certain new inequalities for the sums of factorials are presented.
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables.…
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
We provide, explicitly, equivalences and dual equivalences between categories of abstract quadratic forms theories and subcategories of multifields and multirings, that will bring new perspectives and methods to the abstract theories of…
A new construction, with more visible canonical features, of a qKdV equation in a q-Virasoro context is exhibited.
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
We obtain new closed-form formulas for the moments and absolute moments of the variance-gamma distribution. We thus deduce new formulas for the moments and absolute moments of the product of two correlated zero mean normal random variables.
We introduce a new version of the KL-divergence for Gaussian distributions which is based on Wasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space ${\Bbb R}^n$.…
We study the surface of Gauss double points associated to a very general quartic surface and the natural morphisms associated to it.
A decoupling type inequality for a sum of functions of Guassian vectors is established.
In this work we prove a prime number type theorem involving the normalised Fourier coefficients of holomorphic and Maass cusp forms, using the classical circle method. A key point is in a recent paper of Fouvry and Ganguly, based on…
In this paper we obtain bounds for integer solutions of quadratic polynomials in two variables that represent a natural number. Also we get some results on twin prime numbers. In addition, we use linear functionals to prove some results of…
New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…
We provide new characterizations of two-points and some related distributions. We use properties of independence and/or identity of the distributions of suitable linear forms of random variables. Keywords: characterization of a…
The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
In this paper, we define the notions $q$-birational morphism and $q$-birational divisor and develop the theory about them. We state and prove versions of Kodaira-type vanishing theorem and Zariski decomposition theorem for $q$-birational…
This note provides some new inequalities and approximations for beta distributions, including tail inequalities, exponential inequalities of Hoeffding and Bernstein type, Gaussian inequalities and approximations.