Fields of Interest

• Random matrix theory
• free probability
• Stochastic differential equations
• Stochastic partially differential equations
• Malliavin calculus
• Matrix-valued stochastic processes

Research Paper

1. Wangjun Yuan, Multiple collisions of eigenvalues and singular values of matrix Gaussian field, arXiv:2407.09070.
2. Benoıt Collins, Wangjun Yuan, Strong convergence for tensor GUE random matrices, arXiv:2407.09065.
3. Jian Song, Meng Wang and Wangjun Yuan, On a class of stochastic fractional heat equations, Proceedings AMS (accepted).
4. Jian Song, Meng Wang and Wangjun Yuan, Stochastic partial differential equations associated with Feller processes, arXiv:2310.18726, 2023.
5. 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.
6. Wangjun Yuan, On spectrum of sample covariance matrices from large tensor vectors, ALEA (accepted).
7. Raluca M. Balan and Wangjun Yuan, Hyperbolic Anderson model with time-independent rough noise: Gaussian fluctuations, arXiv:2305.05043, 2023
8. 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.
9. 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.
10. 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.
11. Benoıt 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.
12. Jian Song, Yimin Xiao, and Wangjun Yuan, On eigenvalues of the Brownian sheet matrix, Stochastic Process. Appl. 166 (2023), 104231.
13. Jianfeng Yao and Wangjun Yuan, On eigenvalue distributions of large auto-covariance matrices, Ann. Appl. Probab. 32 (2022), no. 5, 3450-3491.
14. 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.
15. Jian Song, Jianfeng Yao, and Wangjun Yuan, Eigenvalue distributions of high-dimensional matrix processes driven by fractional Brownian motion, Random Matrices Theory Appl. 13 (2024), no.2, Paper No. 2450009, 37 pp.
16. 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. 
17. 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.

Survey

1. Jian Song, Jianfeng Yao, and Wangjun Yuan, Recent advances on eigenvalues of matrix-valued stochastic processes, J. Multivariate Anal. 188 (2022), Paper No. 104847.