Research
Research interest
Random matrix theory, Stochastic differential equations, Stochastic partially differential equations, Matrix-valued stochastic processes, Free probability.
Jian Song, Meng Wang and Wangjun Yuan, On a class of stochastic fractional heat equations, arXiv.2311.12294, 2023.
Jian Song, Meng Wang and Wangjun Yuan, Stochastic partial differential equations associated with Feller processes, arXiv:2310.18726, 2023.
Raluca M. Balan, Jingyu Huang, Xiong Wang, Panqiu Xia, and Wangjun Yuan, Gaussian fluctuations for the wave equation under rough random perturbations, arXiv:2307.00103, 2023.
Wangjun Yuan, On spectrum of sample covariance matrices from large tensor vectors, arXiv:2306.05834, 2023.
Raluca M. Balan and Wangjun Yuan, Hyperbolic Anderson model with time-independent rough noise: Gaussian fluctuations, arXiv:2305.05043, 2023.
Raluca M. Balan and Wangjun Yuan, Central limit theorems for heat equation with time-independent noise: the regular and rough cases, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 26 (2023), no. 2, 2250029. [paper]
Cheuk Yin Lee, Jian Song, Yimin Xiao, and Wangjun Yuan, Hitting probabilities of Gaussian random fields and collision of eigenvalues of random matrices, Trans. Amer. Math. Soc. 376 (2023), no. 6, 4273–4299. [paper]
Raluca M. Balan and Wangjun Yuan, Spatial integral of the solution to hyperbolic Anderson model with time-independent noise, Stochastic Process. Appl. 152 (2022), 177-207. [paper]
Benoît Collins, Jianfeng Yao, and Wangjun Yuan, On spectral distribution of sample covariance matrices from large dimensional and large k-fold tensor products, Electron. J. Probab. 27 (2022), article no. 102, 1-18. [paper]
Jian Song, Yimin Xiao, and Wangjun Yuan, On eigenvalues of the Brownian sheet matrix, Stochastic Process. Appl. 166 (2023), 104231. [paper]
Jianfeng Yao and Wangjun Yuan, On eigenvalue distributions of large auto-covariance matrices, Ann. Appl. Probab. 32 (2022), no. 5, 3450-3491. [paper]
Jian Song, Yimin Xiao, and Wangjun Yuan, On collision of multiple eigenvalues for matrix-valued Gaussian processes, J. Math. Anal. Appl. 502 (2021), no. 2, 125261. [paper]
Jian Song, Jianfeng Yao, and Wangjun Yuan, Eigenvalue distributions of high-dimensional matrix processes driven by fractional Brownian motion, Random Matrices Theory Appl. (Accepted)
Jian Song, Jianfeng Yao, and Wangjun Yuan, High-dimensional central limit theorems for a class of particle systems, Electron. J. Probab. 26 (2021), article no. 87, 1-33. [paper]
Jian Song, Jianfeng Yao, and Wangjun Yuan, High-dimensional limits of eigenvalue distributions for general Wishart process, Ann. Appl. Probab. 30 (2020), no. 4, 1642-1668. [paper]
Survey
Jian Song, Jianfeng Yao, and Wangjun Yuan, Recent advances on eigenvalues of matrix-valued stochastic processes, J. Multivariate Anal. 188 (2022), Paper No. 104847. [paper]
Journal reviewing
Acta Mathematica Scientia, Annals of Probability, Annals of Statistics, Journal of Multivariate Analysis, Journal of Statistical Physics, Statistics and Probability Letters.
Conferences and invited talks
Séminaire Matrices et graphes aléatoires (MEGA). l'Institut Henri Poincaré, Paris, France. April 5, 2024. (Invited talk)
Stochastic Analysis and Statistics 2024. University of Tokyo, Tokyo, Japan. February 6 - 8, 2024. (Invited talk)
2023 Global Young Scholars’ Forum (CUHK-Shenzhen). The Chinese University of Hong Kong-Shenzhen, Shenzhen, China. December 8 - 10, 2023. (Invited talk)
SUSTech Global Forum for Young Mathematicians. Southern University of Science and Technology, Shenzhen, China. November 30, 2023. (Invited talk)
Stochastic Control Seminar (SUSTech). Southern University of Science and Technology, Shenzhen, China. November 2, 2023. (Invited talk)
91st seminar of Long Feng Science Forum (Seminar Series). The Chinese University of Hong Kong-Shenzhen, Shenzhen, China. November 2, 2023. (Invited talk)
The 8th Qilu Youth Forum of Shandong University. Shandong University (Qingdao), Qingdao, China. October 25 - 26, 2023. (Invited talk)
Mathematical Statistics seminar (SU). Stockholm University, Stockholm, Sweden. October 4, 2023. (Invited talk)
Workshop on random matrix theory and high dimensional statistics for complex system. University of Luxembourg, Luxembourg. August 29 - September 1, 2023. (Invited talk)
Probability seminars (USTC). University of Science and Technology of China, Hefei, China. August 9, 2023. (Invited talk)
Probability seminars (SYSU). Sun Yat-sen University, Guangzhou, China. August 4, 2023. (Invited talk)
Probability seminars (GBU). Great Bay University, Dongguan, China. July 25, 2023. (Invited talk)
Probability seminars (SYSU). Sun Yat-sen University, Guangzhou, China. July 20, 2023. (Invited talk)
Probability seminars (CUHK-Shenzhen). The Chinese University of Hong Kong, Shenzhen, Shenzhen, China. July 3, 2023. (Invited talk)
Shenzhen Conference on Random Matrix Theory and Applications. The Chinese University of Hong Kong, Shenzhen, Shenzhen, China. June 26 - 30, 2023. (Invited talk)
International Conference on Malliavin Calculus and Related Topics (Celebrating the work of David Nualart and Anton Thalmaier). University of Luxembourg, Luxembourg. June 12 - 16, 2023. (Poster)
10th International Workshop on Applied Probability. Thessaloniki, Greece. June 7-10, 2023. (Invited talk)
Probability and Mathematical Physics seminar (KTH). KTH Royal Institute of Technology, Stockholm, Sweden. April 4, 2023. (Invited talk)
The 16th German Probability and Statistics Days 2023. University of Duisburg-Essen, Germany. March 7-10, 2023. (Contributed talk)
The 1st Luxembourg Workshop in Stochastic Analysis. University of Luxembourg, Luxembourg. February 15-17, 2023. (Invited talk)
Probability seminars (Shandong University). Shandong University, jinan, China. October 18, 2022. (Invited talk)
The 42nd Conference on Stochastic Processes and their Applications. Wuhan, China. June 27 - July 01, 2022. (Contributed talk)
Workshop on Non-commutative Probability. Kyoto University, Kyoto, Japan. June 22 - 24, 2022. (Invited talk)
Canadian Operator Algebras Symposium, 50th anniversary. University of Ottawa, Ottawa, Canada. May 30 - June 23, 2022. (Contributed talk)
CRM-ISM probability seminar. McGill University, Montreal, Canada. November 24, 2021. (Invited talk)
Statistics and Probability seminars (University of Ottawa). University of Ottawa, Ottawa, Canada. October 15, 2021. (Invited talk)
The 6th Qilu Youth Forum of Shandong University. Shandong University, Shandong, China. September 28 - 30, 2021. (Invited talk)
Workshop on Stochastic modeling: Foundation and Statistics. The University of Hong Kong, Hong Kong, China. August 16, 2021. (Invited talk)
Bernoulli-IMS 10th World Congress in Probability and Statistics. Seoul National University, Seoul, Korea. July 19 - 23, 2021. (Contributed talk)
Workshop on the Theory and Applications of Stochastic Partial Differential Equations. The Fields Institute, Toronto, Canada. June 10 - 14, 2019. (Poster)
Organized workshops and conferences:
Workshop on random matrix theory and high dimensional statistics for complex system, August 29 - September 1, 2023. Co-organized with Mark Podolskij and Chiara Amorino at University of Luxembourg, Luxembourg.