53 citations · 204 across the 25 of their papers we have counts for
14 papers · 1 filter
Gap probability for the hard edge Pearcey process
Dan Dai, Shuai-Xia Xu, Lun Zhang
The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge P…
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 $…
On the deformed Pearcey determinant
Dan Dai, Shuai-Xia Xu, Lun Zhang
In this paper, we are concerned with the deformed Pearcey determinant , where and stands for the tra…
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…
Applications in random matrix theory of a PIII -function sequence from Okamoto's Hamiltonian formulation
Dan Dai, Peter J. Forrester, Shuai-Xia Xu
We consider the singular linear statistic of the Laguerre unitary ensemble consisting of the sum of the reciprocal of the eigenvalues. It is observed that the exponential generatin…
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…
Gap probability at the hard edge for random matrix ensembles with pole singularities in the potential
Dan Dai, Shuai-Xia Xu, Lun Zhang
We study the Fredholm determinant of an integrable operator acting on the interval whose kernel is constructed out of a hierarchy of higher order analogues to the Painlevé…
Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painlevé II system
Shuai-Xia Xu, Dan Dai
We study Fredholm determinants of the Painlevé II and Painlevé XXXIV kernels. In certain critical unitary random matrix ensembles, these determinants describe special gap probabili…
Gaussian unitary ensemble with boundary spectrum singularity and -form of the Painlevé II equation
Xiao-Bo Wu, Shuai-Xia Xu, Yu-Qiu Zhao
We consider the Gaussian unitary ensemble perturbed by a Fisher-Hartwig singularity simultaneously of both root type and jump type. In the critical regime where the singularity app…
Painlevé III asymptotics of Hankel determinants for a perturbed Jacobi weight
Zhao-Yun Zeng, Shuai-Xia Xu, Yu-Qiu Zhao
We study the Hankel determinants associated with the weight where , , , is analytic in a domain containin…
Critical edge behavior in the modified Jacobi ensemble and Painlevé equations
Shuai-Xia Xu, Yu-Qiu Zhao
We study the Jacobi unitary ensemble perturbed by an algebraic singularity at . For fixed , this is the modified Jacobi ensemble studied by Kuijlaars {\it{et al.}} The main…
Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble
Shuai-Xia Xu, Dan Dai, Yu-Qiu Zhao
In this paper, we study the singularly perturbed Laguerre unitary ensemble with , $x\in (0…