26 citations · 59 across the 14 of their papers we have counts for
14 papers
Recurrence Coefficients of the Orthogonal Polynomials for Oscillatory Jacobi-type Weight Functions
Shulin Lyu, Xun Zhou
We study two classes of oscillatory Jacobi-type weight functions , . Other restrictions are imposed on and to…
Hankel Determinant for a Perturbed Laguerre Weight with Pole Singularities and Generalized Painlevé III' Equation
Shulin Lyu, Yuanfei Lyu
We study the Hankel determinant for the weight , with Compared with the weight $x^α…
Ladder Operators for Laguerre-type and Jacobi-type Orthogonal Polynomials
Shulin Lyu, Yuanfei Lyu
In the literature concerning the Laguerre-type weight function , the Jacobi-type weight function , and the shifted Jaco…
Hankel Determinants for a Deformed Laguerre Weight with Multiple Variables and Generalized Painlevé V Equation
Xinyu Mu, Shulin Lyu
We study the Hankel determinant generated by the moments of the deformed Laguerre weight function , where $x\in \left[0,+\infty…
Gap Probability Distribution of Gaussian Unitary Ensembles and Painlevé V Equation
Shengjie Zhang, Shulin Lyu
We consider the Hankel determinant generated by the moments of the even weight function . It is intimatel…
Hankel Determinants for a Gaussian weight with Fisher-Hartwig Singularities and Generalized Painlevé IV Equation
Xinyu Mu, Shulin Lyu
We study the Hankel determinant generated by a Gaussian weight with Fisher-Hartwig singularities of root type at , . It characterizes a type of average characte…
Gaussian Unitary Ensembles with Jump Discontinuities, PDEs and the Coupled Painlevé IV System
Yang Chen, Shulin Lyu
We study the Hankel determinant generated by the Gaussian weight with jump discontinuities at . By making use of a pair of ladder operators satisfied by the associa…
Laguerre Unitary Ensembles with Jump Discontinuities, PDEs and the Coupled Painlevé V System
Shulin Lyu, Yang Chen, Shuai-Xia Xu
We study the Hankel determinant generated by the Laguerre weight with jump discontinuities at . By employing the ladder operator approach to establish Riccati eq…
Gaussian unitary ensemble with two jump discontinuities, PDEs and the coupled Painlevé II and IV systems
Shulin Lyu, Yang Chen
We consider the Hankel determinant generated by the Gaussian weight with two jump discontinuities. Utilizing the results of [C. Min and Y. Chen, Math. Meth. Appl. Sci. {\bf 42} (20…
The Smallest Eigenvalue Distribution of the Jacobi Unitary Ensembles
Shulin Lyu, Yang Chen
In the hard edge scaling limit of the Jacobi unitary ensemble generated by the weight , the probability that all eigenvalues of Hermitian matrices fro…
Asymptotics of the Largest Eigenvalue Distribution of the Laguerre Unitary Ensemble
Shulin Lyu, Chao Min, Yang Chen
We study the probability that all the eigenvalues of Hermitian matrices, from the Laguerre unitary ensemble with the weight $x^γ\mathrm{e}^{-4nx},\;x\in[0,\infty),\;γ>-…
Painlevé III and the Hankel Determinant Generated by a Singularly Perturbed Gaussian Weight
Chao Min, Shulin Lyu, Yang Chen
In this paper, we study the Hankel determinant generated by a singularly perturbed Gaussian weight $$ w(x,t)=\mathrm{e}^{-x^{2}-\frac{t}{x^{2}}},\;\;x\in(-\infty, \infty),\;\;t>0.…
Asymptotic Gap Probability Distributions of the Gaussian Unitary Ensembles and Jacobi Unitary Ensembles
Shulin Lyu, Yang Chen, Engui Fan
In this paper, we address a class of problems in unitary ensembles. Specifically, we study the probability that a gap symmetric about 0, i.e. is found in the Gaussian unit…
The largest eigenvalue distribution of the Laguerre unitary ensemble
Shulin Lyu, Yan Chen
We study the probability that all eigenvalues of the Laguerre unitary ensemble of n by n matrices are between 0 and t, i.e., the largest eigenvalue distribution. Associated with th…