53 citations · 108 across the 26 of their papers we have counts for
27 papers
Asymptotics of Fredholm determinant solutions of the noncommutative Painlevé II equation
Jia-Hao Du, Shuai-Xia Xu, Yu-Qiu Zhao
In this paper, we study the asymptotic behavior of a family of pole-free solutions to the noncommutative Painlevé II equation. These particular solutions can be expressed in terms…
Large time and distance asymptotics of the one-dimensional impenetrable Bose gas and Painlevé IV transition
Zhi-Xuan Meng, Shuai-Xia Xu, Yu-Qiu Zhao
In the present paper, we study the time-dependent correlation function of the one-dimensional impenetrable Bose gas, which can be expressed in terms of the Fredholm determinant of…
Asymptotics of the partition function of the perturbed Gross-Witten-Wadia unitary matrix model
Yu Chen, Shuai-Xia Xu, Yu-Qiu Zhao
We consider the asymptotics of the partition function of the extended Gross-Witten-Wadia unitary matrix model by introducing an extra logarithmic term in the potential. The partiti…
An El-Zahar Type Theorem in -graphs under Codegree Condition
Yangyang Cheng, Mengjiao Rao, Guanghui Wang +1
A -uniform loose cycle, denoted by , is a -graph on vertices whose vertices can be arranged cyclically so that each hyperedge consists of three consecutive vertices,…
Asymptotics of the determinant of the modified Bessel functions and the second Painlevé equation
Yu Chen, Shuai-Xia Xu, Yu-Qiu Zhao
In the paper, we consider the extended Gross-Witten-Wadia unitary matrix model by introducing a logarithmic term in the potential. The partition function of the model can be expres…
On the Fredholm determinant of the confluent hypergeometric kernel with discontinuities
Shuai-Xia Xu, Shu-Quan Zhao, Yu-Qiu Zhao
We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distributi…
Asymptotics of the deformed higher order Airy-kernel determinants and applications
Jun Xia, Yi-Fan Hao, Shuai-Xia Xu +2
We study the one-parameter family of Fredholm determinants , , where stands for the integral operator acting on $L…
Clarkson-McLeod solutions of the fourth Painlevé equation and the parabolic cylinder-kernel determinant
Jun Xia, Shuai-Xia Xu, Yu-Qiu Zhao
The Clarkson-McLeod solutions of the fourth Painlevé equation behave like as , where is some real constant and $D_{α-\fr…
Recent Advances in Asymptotic Analysis
R. Wong, Yu-Qiu Zhao
This is a survey article on an old topic in classical analysis. We present some new developments in asymptotics in the last fifty years. We start with the classical method of Darbo…
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…
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…
Asymptotics of the Charlier polynomials via difference equation methods
Xiao-Min Huang, Yu Lin, Yu-Qiu Zhao
We derive uniform and non-uniform asymptotics of the Charlier polynomials by using difference equation methods alone. The Charlier polynomials are special in that they do not fit i…
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…
Real solutions of the first Painlevé equation with large initial data
Wen-Gao Long, Yu-Tian Li, Sai-Yu Liu +1
We consider three special cases of the initial value problem of the first Painlevé equation (PI). Our approach is based on the method of uniform asymptotics introduced by Bassom, C…
Special functions, integral equations and Riemann-Hilbert problem
R. Wong, Yu-Qiu Zhao
We consider a pair of special functions, and , defined respectively as the solutions to the integral equations \begin{equation*} u(x)=1+\int^\infty_0 \frac {K(t) u(t) dt…
Hankel determinants for a singular complex weight and the first and third Painlevé transcendents
Shuai-Xia Xu, Dan Dai, Yu-Qiu Zhao
In this paper, we consider polynomials orthogonal with respect to a varying perturbed Laguerre weight for and on certain contours in the complex pl…
Proof of a conjecture of Granath on optimal bounds of the Landau constants
Chun-Ru Zhao, Wen-Gao Long, Yu-Qiu Zhao
We study the asymptotic expansion for the Landau constants , \begin{equation*} πG_{n}\sim \ln(16N)+γ+\sum^{\infty}_{k=1}\frac{α_k}{N^k} ~~\mbox{as} ~ n\rightarrow\infty, \end{…
Application of uniform asymptotics to the connection formulas of the fifth Painlevé equation
Zhao-Yun Zeng, Yu-Qiu Zhao
We apply the uniform asymptotics method proposed by Bassom, Clarkson, Law and McLeod to a special Painlevé V equation, and we provide a simpler and more rigorous proof of the conne…
Weights with both absolutely continuous and discrete components: Asymptotics via the Riemann-Hilbert approach
Xiao-Bo Wu, Yu Lin, Shuai-Xia Xu +1
We study the uniform asymptotics for the orthogonal polynomials with respect to weights composed of both absolutely continuous measure and discrete measure, by taking a special cla…
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…
Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point
Xiao-Bo Wu, Yu Lin, Shuai-Xia Xu +1
In this paper, we develop the Riemann-Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an accumulation point. To illustrate our met…
Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight
Shuai-Xia Xu, Dan Dai, Yu-Qiu Zhao
In this paper, we consider the Hankel determinants associated with the singularly perturbed Laguerre weight , , and . When the matr…
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…