We summarize significant classical results on (in) determinacy of measures in terms of their
finite positive integer order moments. Well known is the role of the smallest eigenvalues of …

An asymptotic expression of the orthonormal polynomials PN (z) as N→∞, associated with
the singularly perturbed Laguerre weight w α (x; t)= x α e− x− tx, x∈[0,∞), α>− 1, t≥ 0⁠, is …

An asymptotic expression for the polynomials $\mathcal {P} _n (z) $, $ z\notin (-\infty,\infty) $,
orthonormal with respect to a singularly perturbed Gaussian weight, $\exp (-z^ 2-t/z^ 2),~ z\in …

We study the asymptotic behavior of the smallest eigenvalue, λ N, of the Hankel (or
moments) matrix denoted by, with respect to the weight. An asymptotic expression of the …

In this paper, we study the large N behavior of the smallest eigenvalue λ N of the (N+ 1)×(N+
1) Hankel matrix, HN=(μ j+ k) 0≤ j, k≤ N, generated by the γ dependent Jacobi weight w (z …

Krylov subspace method is an effective method for large-scale eigenproblems. The shift-and-
invert Arnoldi method is employed to compute a few eigenpairs of a large Hankel matrix …

The smallest eigenvalue of large Hankel matrices associated with a semiclassical Laguerre
weight Page 1 M athematical I nequalities & A pplications Volume 27, Number 1 (2024), 53–62 …

In this thesis, we study three problems in random matrices, which are closely related to
orthogonal polynomials and Painlevé equations. The first problem is a follow-up of a paper …

In this paper, we focus on the properties of the recurrence coefficients βn (t; α) of orthogonal
polynomials with respect to a deformed octic Freud weight w (x; t, α)=| x| αe− x8+ tx2, x, t∈ …