We study the fluctuations of linear statistics with polynomial test functions for Multiple Orthogonal Polynomial Ensembles. Ensembles form an important class determinantal point processes that include random matrix models such as GUE external source, complex Wishart matrices, multi-matrix and others. Our analysis is based on recurrence multiple orthogonal polynomials, constructed out nearest ne...

We obtain the time-dependent correlation function describing the evolution of a single spin excitation state in a linear spin chain with isotropic nearestneighbour XY coupling, where the Hamiltonian is related to the Jacobi matrix of a set of orthogonal polynomials. For the Krawtchouk polynomial case, an arbitrary element of the correlation function is expressed in a simple closed form. Its asy...

The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments. Moment and cumulant generating functions are then derived and represented in terms of polygamma functions. The behaviour of shape parameters, namely kurtosis and entropy, is investigated. In add...

In this paper, we introduce a bivariate Kantorovich variant of combination of Szász and Chlodowsky operators based on Charlier polynomials. Then, we study local approximation properties for these operators. Also, we estimate the approximation order in terms of Peetre's K-functional and partial moduli of continuity. Furthermore, we introduce the associated GBS-case (Generalized Boolean Sum) of t...

Abstract: This paper carries out an investigation of the orthogonal-polynomial approach to reshaping symmetric distributions to fit in with data requirements so as to cover the multivariate case. With this objective in mind, reference is made to the class of spherical distributions, given that they provide a natural multivariate generalization of univariate even densities. After showing how to ...

We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the depend...

Given a stochastic process X = {Xt, t ∈ R+} with finite moments of convenient order, a time–space harmonic polynomial relative to X is a polynomial Q(x, t) such that the process Mt =Q(Xt, t) is a martingale with respect to the filtration associated with X . Major examples are the Hermite polynomials relative to a Brownian motion, the Charlier polynomials relative to a Poisson process and the La...

The probability density function (PDF) of a random variable associated with the solution partial differential equation (PDE) parameters is approximated using truncated series expansion. PDE solved two stochastic finite element methods, Monte Carlo sampling and Galerkin method global polynomials. functional PDE, such as average over physical domain. are obtained considering number terms in Gram-...