13 citations · 42 across the 9 of their papers we have counts for
9 papers
Orthogonal polynomials: from Heun equations to Painlevé equations
Mengkun Zhu, Yuting Chen, Jianduo Yu +1
In this paper, we {\color{black}study four kinds of polynomials orthogonal with the singularly perturbed Gaussian weight , the deformed Freud weight …
Painlevé V for a Jacobi unitary ensemble with random singularities
Mengkun Zhu, Chuanzhong Li, Yang Chen
In this paper, we focus on the relationship between the fifth Painlevé equation and a Jacobi weight perturbed with random singularities, \begin{equation*} w(z)=\left(1-z^2\right)^α…
Painlevé IV, Form and the Deformed Hermite Unitary Ensembles
Mengkun Zhu, Dan Wang, Yang Chen
We study the Hankel determinant generated by a deformed Hermite weight with one jump , where , , , $γ>-1…
The smallest eigenvalue of large Hankel matrices generated by a singularly perturbed Laguerre weight
Mengkun Zhu, Yang Chen, Chuanzhong Li
An asymptotic expression of the orthonormal polynomials as , associated with the singularly perturbed Laguerre weight $w_α(x;t)=x^α{\rm e}^…
Smallest Eigenvalue of Large Hankel Matrices at Critical Point: Comparing Conjecture With Parallelised Computation
Yang Chen, Jakub Sikorowski, Mengkun Zhu
We propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned matrices. It is based on the {\it LDLT} decomposition and involve…
The Smallest Eigenvalue of Large Hankel Matrices
Mengkun Zhu, Yang Chen, Niall Emmart +1
We investigate the large behavior of the smallest eigenvalue, , of an Hankel (or moments) matrix , generated b…
The Smallest Eigenvalue of Large Hankel Matrices Generated by a Deformed Laguerre Weight
Mengkun Zhu, Niall Emmart, Yang Chen +1
We study the asymptotic behavior of the smallest eigenvalue, , of the Hankel (or moments) matrix denoted by , with re…
On properties of a deformed Freud weight
Mengkun Zhu, Yang Chen
We study the recurrence coefficients of the monic polynomials orthogonal with respect to the deformed (also called semi-classical) Freud weight \begin{equation*} w_α(x;s,N…
Center of mass distribution of the Jacobi unitary ensembles: Painleve V, asymptotic expansions
Longjun Zhan, Gordon Blower, Yang Chen +1
In this paper, we study the probability density function, , of the center of mass of the finite Jacobi unitary ensembles with parameters and…