个人网站 (Personal website, en): jiyuanzhangmath [dot] github [dot] io
研究方向
从事随机矩阵理论中,具有(正交、酉、辛等)群不变性的随机矩阵模型极限行为的研究。目前主要感兴趣的科学问题有:
(1)具有群不变性的行列式点过程,在矩阵阶数趋向无穷时的极限行为;
(2)Dyson指数的推广以及经典概率论、自由概率论、有限自由概率论之间的中介理论;
(3)具有重尾分布的随机矩阵的渐近行为。
招生意向
访问学者:随机矩阵、正交多项式、自由概率论方向(长期有效;条件薪酬面议)
博士后:随机矩阵、正交多项式、自由概率论方向(长期有效;条件薪酬面议)
硕士:基础数学专业(长期有效;欢迎创新、强基、保研或考研机制)
联系方式
E-mail: jiyuanzhang [at] scut [dot] edu [dot] cn
办公室:华南理工大学五山校区4号楼4140
工作经历
2025年至今:华南理工大学,副教授
2022年至2025年:比利时荷语区鲁汶大学,博士后
教育背景
2018年至2022年:澳大利亚墨尔本大学,博士
2016年至2017年:澳大利亚墨尔本大学,硕士
2011年至2015年:中山大学,学士
科研成果
Preprints
Mario Kieburg, Jiyuan Zhang. A rate of convergence when generating stable invariant Hermitian random matrix ensembles. arXiv:2302.06968.
Mario Kieburg, Jiyuan Zhang. Stable distributions and domains of attraction for unitarily invariant Hermitian random matrix ensembles. Accepted by Annales de l’institut Henri Poincare (B) Probability and Statistics. arXiv:2110.14877.
Publications
Peter J. Forrester, Mario Kieburg, Shi-Hao Li, Jiyuan Zhang. Dip-ramp-plateau for Dyson Brownian motion from the identity on U(N). Prob. Math. Phys. 5 (2024) 321-355.
Kieburg, Mario; Li, Shi-Hao; Zhang, Jiyuan; Forrester, Peter J. Cyclic Pólya ensembles on the unitary matrices and their spectral statistics. Constr. Approx.57(2023), no.3, 1063–1108.
Kieburg, Mario; Zhang, Jiyuan. Derivative principles for invariant ensembles. Adv. Math.413(2023), Paper No. 108833, 52 pp.
Zhang, Jiyuan; Kieburg, Mario; Forrester, Peter J. Harmonic analysis for rank-1 randomised Horn problems. Lett. Math. Phys.111(2021), no.4, Paper No. 98, 27 pp.
Forrester, Peter J.; Zhang, Jiyuan. Corank-1 projections and the randomised Horn problem. Tunis. J. Math. 3 (2021), no. 1, 55–73.
Forrester, Peter J., and Jiyuan Zhang. Parametrising Correlation Matrices. Journal of Multivariate Analysis, vol. 178, 2020, p. 104619.
Forrester, P. J., and Jiyuan Zhang. Lyapunov Exponents for Some Isotropic Random Matrix Ensembles. Journal of Statistical Physics, 2020, pp. 1–18.
Forrester, P.J. and Zhang, J., 2018. Volumes and distributions for random unimodular complex and quaternion lattices. Journal of Number Theory, 190, pp.1-39.
N. Magyar, J. Verniero, A. Szabo, J. Zhang and T. Van Doorsselaere1. Solar wind data analysis aided by synthetic modeling: A better understanding of plasma frame variations from temporal data. A&A, 688 (2024) A74