24 citations · 185 across the 18 of their papers we have counts for
18 papers
Asymptotic Properties of Some Freud Polynomials
Chao Min, Liwei Wang, Yang Chen
We study the asymptotic properties of monic orthogonal polynomials (OPs) with respect to some Freud weights when the degree of the polynomial tends to infinity, including the asymp…
Differential and Difference Equations for Recurrence Coefficients of Orthogonal Polynomials with a Singularly Perturbed Laguerre-type Weight
Chao Min, Yuan Cheng, Yang Chen
We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated s…
Painlevé IV, Chazy II, and Asymptotics for Recurrence Coefficients of Semi-classical Laguerre Polynomials and Their Hankel Determinants
Chao Min, Yang Chen
This paper studies the monic semi-classical Laguerre polynomials based on previous work by Boelen and Van Assche \cite{Boelen}, Filipuk et al. \cite{Filipuk} and Clarkson and Jorda…
Hankel Determinant and Orthogonal Polynomials for a Perturbed Gaussian Weight: from Finite to Large Asymptotics
Chao Min, Yang Chen
We study the monic polynomials orthogonal with respect to a symmetric perturbed Gaussian weight wher…
Semi-classical Jacobi Polynomials, Hankel Determinants and Asymptotics
Chao Min, Yang Chen
We study orthogonal polynomials and Hankel determinants generated by a symmetric semi-classical Jacobi weight. By using the ladder operator technique, we derive the second-order no…
Global and Local Scaling Limits for Linear Eigenvalue Statistics of Jacobi -Ensembles
Chao Min, Yang Chen
We study the moment-generating functions (MGF) for linear eigenvalue statistics of Jacobi unitary, symplectic and orthogonal ensembles. By expressing the MGF as Fredholm determinan…
Differential, Difference and Asymptotic Relations for Pollaczek-Jacobi Type Orthogonal Polynomials and Their Hankel Determinants
Chao Min, Yang Chen
In this paper, we study the orthogonal polynomials with respect to a singularly perturbed Pollaczek-Jacobi type weight $$ w(x,t):=(1-x^2)^α\mathrm{e}^{-\frac{t}{1-x^{2}}},\qquad x\…
Painlevé V and the Hankel Determinant for a Singularly Perturbed Jacobi Weight
Chao Min, Yang Chen
We study the Hankel determinant generated by a singularly perturbed Jacobi weight I…
Asymptotics of the Largest Eigenvalue Distribution of the Laguerre Unitary Ensemble
Shulin Lyu, Chao Min, Yang Chen
We study the probability that all the eigenvalues of Hermitian matrices, from the Laguerre unitary ensemble with the weight $x^γ\mathrm{e}^{-4nx},\;x\in[0,\infty),\;γ>-…
Painlevé VI, Painlevé III and the Hankel Determinant Associated with a Degenerate Jacobi Unitary Ensemble
Chao Min, Yang Chen
This paper studies the Hankel determinant generated by a perturbed Jacobi weight, which is closely related to the largest and smallest eigenvalue distribution of the degenerate Jac…
Painlevé V, Painlevé XXXIV and the Degenerate Laguerre Unitary Ensemble
Chao Min, Yang Chen
In this paper, we study the Hankel determinant associated with the degenerate Laguerre unitary ensemble. This problem originates from the largest or smallest eigenvalue distributio…
Painlevé III and the Hankel Determinant Generated by a Singularly Perturbed Gaussian Weight
Chao Min, Shulin Lyu, Yang Chen
In this paper, we study the Hankel determinant generated by a singularly perturbed Gaussian weight $$ w(x,t)=\mathrm{e}^{-x^{2}-\frac{t}{x^{2}}},\;\;x\in(-\infty, \infty),\;\;t>0.…
Linear Statistics of Random Matrix Ensembles at the Spectrum Edge Associated with the Airy Kernel
Chao Min, Yang Chen
In this paper, we study the large behavior of the moment-generating function (MGF) of the linear statistics of Hermitian matrices in the Gaussian unitary, symplecti…
Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite to Double Scaling
Chao Min, Yang Chen
In this paper, we study the gap probability problem of the (symmetric) Jacobi unitary ensemble of Hermitian random matrices, namely the probability that the interval $(-a,a)\:(0<a<…
Painlevé Transcendents and the Hankel Determinants Generated by a Discontinuous Gaussian Weight
Chao Min, Yang Chen
This paper studies the Hankel determinants generated by a discontinuous Gaussian weight with one and two jumps. It is an extension of Chen and Pruessner \cite{Chen2005}, in which t…
On the variance of linear statistics of Hermitian random matrices
Chao Min, Yang Chen
Linear statistics, a random variable build out of the sum of the evaluation of functions at the eigenvalues of a N times N random matrix,sum[j=1 to N]f(xj) or tr f(M), is an ubiqui…
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…
Linear Statistics of Matrix Ensembles in Classical Background
Yang Chen, Chao Min
Given a joint probability density function of real random variables, obtained from the eigenvector-eigenvalue decomposition of random matrices,…