7 papers
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…
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<…