个人简介

       赵育求，中山大学理学院教授，博士生导师。研究方向为复分析和渐近分析。目前主要研究兴趣包括: Riemann-Hilbert方法及其应用；随机矩阵理论及其它数学物理问题；特殊函数与正交多项式；Painleve方程, Heun方程及相关差分方程。现为国际SCI数学刊物Complex Variables and Elliptic Equations编委。

教育背景

1991.9-1994.7，中山大学数学系，博士 

1981.9-1988.7，中山大学数学系，本科/硕士

工作经历

2025.4-至今，中山大学理学院，教授

2004.11-2025.4，中山大学数学学院，教授

1997.9-2004.10，中山大学数学学院，副教授

1996.1-1997.9，中山大学数学学院，讲师

访学经历

2008.2-2009.2, 香港城市大学, 访问学者

1998.7-2000.7, 香港城市大学, 访问学者

1996.9-1997.9, 香港城市大学, 访问学者

2003.9-2004.3, 美国加州大学圣地亚哥分校, 访问学者

主持的部分科研项目

国家基金面上项目（12371077），Painlevé函数局部-整体性质及其应用

国家基金面上项目（11971489），Painlevé方程及Heun方程的匹配问题和连接公式 

国家基金面上项目（11571375），随机矩阵理论与Painleve方程若干问题研究 

国家基金面上项目（10871212），非交换最速下降法的一致渐近研究

国家基金面上项目（10471154），最速下降法及若干相关问题研究 

发表论文

#表示共同第一作者，*表示通讯作者

[1] Asymptotics of Fredholm determinant solutions of the noncommutative Painlevé II equation, to appear in  Anal. Appl. (with Jia-Hao Du and Shuai-Xia Xu, arXiv:2505.16830).

[2]Large time and distance asymptotics of the one-dimensional impenetrable Bose gas and Painlevé IV transition, Phys. D 475 (2025), Paper No. 134589, 20 pp (with Zhi-Xuan Meng and Shuai-Xia Xu, arXiv:2505.16780).

[3]Asymptotics of the partition function of the perturbed Gross-Witten-Wadia unitary matrix model, Stud. Appl. Math.  153 (2024), Paper No. e12762, 40 pp (with Yu Chen and Shuai-Xia Xu, arXiv:2505.16739).

[4]Asymptotics of the determinant of the modified Bessel functions and the second Painlevé equation, Random Matrices Theory Appl.  13 (2024), Paper No. 2450003, 43 pp (with Yu Chen and Shuai-Xia Xu, arXiv:2402.11233).

[5]On the Fredholm determinant of the confluent hypergeometric kernel with discontinuities, Phys. D 461 (2024), Paper No. 134101, 23 pp (with Shuai-Xia Xu and Shu-Quan Zhao, arXiv:2402.11214).

[6]Asymptotics of the deformed higher order Airy-kernel determinants and applications, Nonlinearity 36 (2023), 4384-4424 (with Jun Xia, Yi-Fan Hao, Shuai-Xia Xu and Lun Zhang, arXiv:2306.14835).

[7]Clarkson-McLeod solutions of the fourth Painlevé equation and the parabolic cylinder-kernel determinant, J. Differential Equations 352 (2023), 249-307 (with Jun Xia and Shuai-Xia Xu, arXiv:2301.05807).

[8]Recent advances in asymptotic analysis, Anal. Appl.  20 (2022), 1103-1146 (with R. Wong, arXiv:2204.09305).

[9]Singular asymptotics for the Clarkson-McLeod solutions of the fourth Painlevé equation, Phys. D 434 (2022), Paper No. 133254, 18 pp (with Jun Xia and Shuai-Xia Xu, arXiv:2204.00733).

[10]Isomonodromy sets of accessory parameters for Heun class equations, Stud. Appl. Math. 146 (2021), 901-952 (with Jun Xia and Shuai-Xia Xu, arXiv:2101.02864). 

[11]Asymptotics of the Charlier polynomials via difference equation methods, Anal. Appl.  19 (2021), 679-713 (with Xiao-Min Huang and Yu Lin, arXiv:1901.06041).

[12]Gap probability of the circular unitary ensemble with a Fisher-Hartwig singularity and the coupled Painlevé V system， Comm. Math. Phys. 377 (2020), 1545-1596 (with Shuai-Xia Xu, arXiv:1907.11509). 

[13]Gaussian unitary ensemble with boundary spectrum singularity and σ-form of the Painlevé II equation, Stud. Appl. Math. 140 (2018), 221-251 (with Xiao-Bo Wu and Shuai-Xia Xu, arXiv:1706.03174).

[14]Real solutions of the first Painlevé equation with large initial data, Stud. Appl. Math. 139 (2017), 505-532 (with Wen-Gao Long, Yu-Tian Li and Sai-Yu Liu, arXiv:1612.01350).

[15]Special functions, integral equations and Riemann-Hilbert problem, Proc. Amer. Math. Soc. 144 (2016), 4367-4380 (with R. Wong, arXiv:1603.05357).

[16]Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point, Anal. Appl. 14 (2016), 705-737 (with Xiao-Bo Wu, Yu Lin and Shuai-Xia Xu, arXiv:1410.3948).

[17]Plancherel-Rotach type asymptotics of the sieved Pollaczek polynomials via the Riemann-Hilbert approach, J. Approx. Theory 208 (2016), 21–58 (with Xiao-Bo Wu, Yu Lin and Shuai-Xia Xu, arXiv:1412.8580).

[18]Hankel determinants for a singular complex weight and the first and third Painlevé transcendents, J. Approx.Theory 205 (2016), 64-92 (with Shuai-Xia Xu and Dan Dai, arXiv:1509.07015).

[19]Proof of a conjecture of Granath on optimal bounds of the Landau constants, J. Approx. Theory 204 (2016), 17-33 (with Chun-Ru Zhao and Wen-Gao Long, arXiv:1505.00304).

[20]Application of uniform asymptotics to the connection formulas of the fifth Painlevé equation, Appl. Anal. 95 (2016), 390-404 (with Zhao-Yun Zeng, arXiv:1501.00337).

[21]Painlevé III asymptotics of Hankel determinants for a perturbed Jacobi weight, Stud. Appl. Math. 135 (2015), 347-376 (with Zhao-Yun Zeng and Shuai-Xia Xu, arXiv:1412.8586).

[22]Critical edge behavior in the modified Jacobi ensemble and Painlevé equations, Nonlinearity 28 (2015) 1633-1674  (with Shuai-Xia Xu, arXiv:1404.5105).

[23]Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight, J. Approx. Theory.  192 (2015) 1-18 (with Shuai-Xia Xu and Dan Dai, arXiv:1407.7334).

[24]Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble, Comm. Math. Phys. 332 (2014), 1257-1296 (with Shuai-Xia Xu and Dan Dai, arXiv:1309.4354).

[25]Asymptotics of Landau constants with optimal error bounds, Constr. Approx. 40 (2014), 281-305 (with Yutian Li, Saiyu Liu and Shuaixia Xu, arXiv:1309.4564).

[26]High-frequency uniform asymptotics for the Helmholtz equation in a quarter-plane, Asymptot. Anal. 84 (2013), 1-15 (with Min-Hai Huang).

[27]Critical edge behavior in the modified Jacobi ensemble and the Painlevé V transcendents, J. Math. Phys. 54 (2013), 083304, 29 pp (with Shuai-Xia Xu).

[28]The uniqueness and existence of solutions for the 3D Helmholtz equation in a stratified medium with unbounded perturbation, Math. Methods Appl. Sci. 36 (2013), 2033-2047 (with Lihan Liu, Yuehai Qin and Yongzhi Xu).

[29]Uniform treatment of Darboux's method and the Heisenberg polynomials, Proc. Amer. Math. Soc. 141 (2013), 2683-2691 (with Sai-Yu Liu and R.Wong, arXiv:1305.5044).

[30]Asymptotics of discrete Painlevé V transcendents via the Riemann-Hilbert approach, Stud. Appl. Math. 130 (2013), 201-231 (with Shuaixia Xu).

[31]Full asymptotic expansions of the Landau constants via a difference equation approach, Appl. Math. Comput. 219 (2012), 988-995 (with Yutian Li, Saiyu Liu and Shuaixia Xu).

[32]The uniqueness and existence of solutions for the 3D Helmholtz equation in a step-index waveguide with unbounded perturbation, Math. Methods Appl. Sci. 35 (2012), 857-868 (with Lihan Liu, Yuehai Qin and Yongzhi Xu).

[33]Uniform asymptotics of a system of Szego class polynomials via the Riemann-Hilbert approach, Anal. Appl. 9 (2011), 447-480 (with Jian-Rong Zhou and Shuai-Xia Xu).

[34]High-frequency asymptotics for the modified Helmholtz equation in a quarter-plane, Appl. Anal. 90 (2011), 1927-1938 (with Min-Hai Huang).

[35]Universality for eigenvalue correlations from the unitary ensemble associated with a family of singular weights, J. Math. Phys. 52 (2011), 093302, 14 pp (with Shuai-Xia Xu and Jian-Rong Zhou).

[36]Asymptotic distributions of the zeros of certain classes of Gauss hypergeometric polynomials, Appl. Math. Comput. 218 (2011), 1153-1159 (with Jian-Rong Zhou).

[37]Painlevé XXXIV asymptotics of orthogonal polynomials for the Gaussian weight with a jump at the edge, Stud. Appl. Math. 127 (2011), 67-105 (with Shuai-Xia Xu).

[38]Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach, Sci. China Math. 54 (2011), 661-679 (with Shuai-Xia Xu).

[39]Uniform asymptotics and zeros of a system of orthogonal polynomials defined via a difference equation, J. Math. Anal. Appl. 369 (2010), 453-472 (with Hong-Yong Wang).

[40]Asymptotics of orthogonal polynomials via the Riemann-Hilbert approach, Acta Math. Sci. Ser. B Engl. Ed. 29 (2009), 1005-1034 (with R.Wong).

[41]Uniform asymptotics of the Pollaczek polynomials via the Riemann-Hilbert approach, Proc. R. Soc. Lond. Ser. A 464 (2008), 2091-2112 (with Jian-Rong Zhou).

[42]A uniform asymptotic expansion for Jacobi polynomials via uniform treatment of Darboux's method, J. Approx. Theory 148 (2007), 1-11 (with Xiao-Xi Bai).

[43]An infinite asymptotic expansion for the extreme zeros of the Pollaczek polynomials, Stud. Appl. Math. 118 (2007), 255-279 (with Jian-Rong Zhou).

[44]Uniform asymptotics for orthogonal polynomials via the Riemann-Hilbert approach, Appl. Anal. 85 (2006), 1165-1176.

[45]Uniform asymptotic expansions of the Pollaczek polynomials, J. Comput. Appl. Math. 190 (2006), 37-56 (with Jian-Rong Zhou).

[46]On a uniform treatment of Darboux's method, Constr. Approx. 21 (2005), 225-255 (with R. Wong).

[47]Uniform asymptotic expansion of the Jacobi polynomials in a complex domain, Proc. R. Soc. Lond. Ser. A 460 (2004), 2569-2586 (with R. Wong).

[48]Estimates for the error term in a uniform asymptotic expansion of the Jacobi polynomials, Anal. Appl. 1 (2003), 213-241 (with R. Wong).

[49]A uniform asymptotic expansion of the single variable Bell polynomials, J. Comput. Appl. Math. 150 (2003), 329-355.

[50]Exponential asymptotics of the Mittag-Leffler function, Constr. Approx. 18 (2002), 355-385 (with R. Wong).

[51]Gevrey asymptotics and Stieltjes transforms of algebraically decaying functions, R. Soc. Lond. Proc. Ser. A 458 (2002), 625-644 (with R. Wong).

[52]Smoothing of Stokes's discontinuity for the generalized Bessel function. II, R. Soc. Lond. Proc. Ser. A 455 (1999), 3065-3084 (with R. Wong).

[53]Smoothing of Stokes's discontinuity for the generalized Bessel function, R. Soc. Lond. Proc. Ser. A 455 (1999), 1381-1400 (with R. Wong).

[54]Bi-analytic functions and their applications in elasticity,  Partial differential and integral equations (Newark, DE, 1997), 233-247, ISAAC, 2, Kluwer Acad. Publ., Dordrecht, 1999  (with Wei Lin).

[55]On the plane stress boundary value problem of quasi-static linear thermoelasticity, Acta Math. Appl. Sinica (English Ser.) 13 (1997), 385-394 (with Wei Lin).

[56]On the plane orthotropic stress problem of quasi-static thermoelasticity, J. Elasticity 46 (1997), 199-216.

[57]Normal modes analysis for sound waves in an ocean with an ice cap and a perfectly reflecting bottom, Appl. Anal. 63 (1996), 167-181 (with Wei Lin and Yongzhi Xu).

[58]An exact solution to the plane orthotropic elasticity problem with rectangular boundaries under arbitrary edge forces, Philos. Trans. Roy. Soc. London Ser. A 354 (1996), 2469-2511.

[59]Numerical solution to problems concerning quasi-static thermoelasticity, Appl. Anal. 57 (1995), 221-234 (with Wei Lin).

[60]On the plane problem of orthotropic quasi-static thermoelasticity, J. Elasticity 41 (1995), 161-175 (with Wei Lin).

[61]On plane displacement boundary value problem of quasi-static linear thermoelasticity, Appl. Anal. 56 (1995), 117-129.

[62]The proof of Goka's conjecture, IEEE Trans. Automat. Control 31 (1986), 972–973.ntrol 31 (1986), 972–973.