6 citations · 6 across the 3 of their papers we have counts for
9 papers
Singular asymptotics for the Clarkson-McLeod solutions of the fourth Painlevé equation
Jun Xia, Shuai-Xia Xu, Yu-Qiu Zhao
We consider the Clarkson-McLeod solutions of the fourth Painlevé equation. This family of solutions behave like as , where $…
Isomonodromy sets of accessory parameters for Heun class equations
Jun Xia, Shuai-Xia Xu, Yu-Qiu Zhao
In this paper, we consider the monodromy and, in particularly, the isomonodromy sets of accessory parameters for the Heun class equations. We show that the Heun class equations can…
Asymptotics of Fredholm determinant associated with the Pearcey kernel
Dan Dai, Shuai-Xia Xu, Lun Zhang
The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue dens…
On integrals of the tronquée solutions and the associated Hamiltonians for the Painlevé II equation
Dan Dai, Shuai-Xia Xu, Lun Zhang
We consider a family of tronquée solutions of the Painelvé II equation \begin{equation*} q''(s)=2q(s)^3+sq(s)-(2α+\frac12), \qquad α> -\frac12, \end{equation*} which is characteriz…
Gap probability of the circular unitary ensemble with a Fisher-Hartwig singularity and the coupled Painlevé V system
Shuai-Xia Xu, Yu-Qiu Zhao
We consider the circular unitary ensemble with a Fisher-Hartwig singularity of both jump type and root type at . A rescaling of the ensemble at the Fisher-Hartwig singularity…
Gaussian unitary ensembles with pole singularities near the soft edge and a system of coupled Painlevé XXXIV equations
Dan Dai, Shuai-Xia Xu, Lun Zhang
In this paper, we study the singularly perturbed Gaussian unitary ensembles defined by the measure \begin{equation*} \frac{1}{C_n} e^{- n\textrm{tr}\, V(M;λ,\vec{t}\;)}dM, \end{equ…