Related papers: Relative asymptotics for orthogonal matrix polynom…
Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in…
We construct a new type of convergent asymptotic representations, dyadic factorial expansions. Their convergence is geometric and the region of convergence can include Stokes rays, and often extends down to 0^+. For special functions such…
Originally, Tur\'{a}n's inequality states that if $(P_n(x))_{n\in\mathbb{N}_0}$ is the sequence of Legendre polynomials, then $\Delta_n(x):=P_n^2(x)-P_{n+1}(x)P_{n-1}(x)\geq0$ for all $n\in\mathbb{N}$ and $x\in[-1,1]$. Gasper specified the…
Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information Theory, etc. The purpose of the article is pedagogical, it begins by recalling detailed…
This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature…
We consider expansions of products of theta-functions associated with arbitrary root systems in terms of nonsymmetric Macdonald polynomials at $t=\infty$ divided by their norms. The latter are identified with the graded characters of…
The classical Painlev\'e equations are so well known that it may come as a surprise to learn that the asymptotic description of its solutions remains incomplete. The problem lies mainly with the description of families of solutions in the…
A class of orthogonal polynomials associated with Coulomb wave functions is introduced. These polynomials play a role analogous to that the Lommel polynomials do in the theory of Bessel functions. The measure of orthogonality for this new…
We study a family of monic orthogonal polynomials which are orthogonal with respect to the varying, complex valued weight function, $\exp(nsz)$, over the interval $[-1,1]$, where $s\in\mathbb{C}$ is arbitrary. This family of polynomials…
In this paper, we study the asymptotics of the discrete Chebyshev polynomials tn (z, N) as the degree grows to infinity. Global asymptotic formulas are obtained as n \rightarrow \infty, when the ratio of the parameters n/N = c is a constant…
Polynomial ensembles are determinantal point processes associated with (non necessarily orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put forward the use of recurrence coefficients to obtain the…
We consider the asymptotics of orthogonal polynomials for measures that are differentiable, but not necessarily analytic, multiplicative perturbations of Jacobi-like measures supported on disjoint intervals. We analyze the Fokas-Its-Kitaev…
We apply a symbolic approach of the general quadratic decomposition of polynomial sequences - presented in a previous article referenced herein - to polynomial sequences fulfilling specific orthogonal conditions towards two given…
We investigate the ratio asymptotic behavior of the sequence $(Q_{n})_{n=0}^{\infty}$ of multiple orthogonal polynomials associated with a Nikishin system of $p\geq 1$ measures that are compactly supported on the star-like set of $p+1$ rays…
Symmetric Jack polynomials arise naturally in several contexts, including statistics, physics, combinatorics, and representation theory. They are pairwise orthogonal with repsect to two different inner products, the first defined by…
This paper analyzes the concept of orthogonality in second-order polynomial sequences that have Binet formula similar to that of the Fibonacci and Lucas numbers, referred to as Generalized Fibonacci Polynomials (GFP). We give a technique to…
Let $X=\{X_t, t\ge0\}$ be a c\`{a}dl\`{a}g L\'{e}vy process, centered, with moments of all orders. There are two families of orthogonal polynomials associated with $X$. On one hand, the Kailath--Segall formula gives the relationship between…
Starting from Montgomery's conjecture, there has been a substantial interest on the connections of random matrix theory and the theory of L-functions. In particular, moments of characteristic polynomials of random matrices have been…
Classical Gon\v{c}arov polynomials are polynomials which interpolate derivatives. Delta Gon\v{c}arov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental…
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed…