何煜坤 (He Yukun)

Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University

Address: 2005 Songhu Road, Shanghai, China

Office: 551

Email: heyukun@fudan.edu.cn

Research

  1. Bulk universality of random regular graphs, with Jiaoyang Huang and Xiaoyu Wang. Preprint arXiv: 2610.08127.
  2. On eigenvectors of the SYK model. Preprint arXiv: 2609.35024.
  3. The oriented Kesten–McKay law for random regular digraphs, with Jiaoyang Huang. Preprint arXiv: 2609.05297.
  4. Free energy and spectral edge of the SYK model. Preprint arXiv: 2607.18998.
  5. Gaussian Waves and Edge Eigenvectors of Random Regular Graphs, with Jiaoyang Huang and Horng-Tzer Yau. Preprint arXiv: 2502.08897, to appear in Annals of Probability.
  6. Extremal eigenvectors of sparse random matrices, with Jiaoyang Huang and Chen Wang. Probability Theory and Related Fields, 196 (2026), 1481–1538.
  7. Edge universality of sparse Erdős–Rényi digraphs. Probability Theory and Related Fields, 195 (2026), 1505–1557.
  8. Spectral gap and edge universality of dense random regular graphs. Communications in Mathematical Physics, 405 (2024), Paper No. 181, 40 pp.
  9. Quantitative CLT for linear eigenvalue statistics of Wigner matrices, with Zhigang Bao. Annals of Applied Probability, 33 (2023), 5171-5207.
  10. Fluctuations of extreme eigenvalues of sparse Erdős–Rényi graphs, with Antti Knowles. Probability Theory and Related Fields, 180 (2021), 985-1056.
  11. On Cramér–von Mises statistic for the spectral distribution of random matrices, with Zhigang Bao. Annals of Applied Probability, 32 (2022), 4315-4355.
  12. Bulk eigenvalue fluctuations of sparse random matrices. Annals of Applied Probability, 30 (2020), 2846-2879.
  13. Local law and complete eigenvector delocalization for supercritical Erdős–Rényi graphs, with Antti Knowles and Matteo Marcozzi. Annals of Probability, 47 (2019), 3278-3302.
  14. Mesoscopic Eigenvalue Density Correlations of Wigner Matrices, with Antti Knowles. Probability Theory and Related Fields, 177 (2020), 147-216.
  15. Diffusion Profile for Random Band Matrices: a Short Proof, with Matteo Marcozzi. Journal of Statistical Physics, 177 (2019), 666-716.
  16. Mesoscopic linear statistics of Wigner matrices of mixed symmetry class. Journal of Statistical Physics, 175 (2019), 932-959.
  17. Isotropic self-consistent equations for mean-field random matrices, with Antti Knowles and Ron Rosenthal. Probability Theory and Related Fields, 171 (2018), 203-249.
  18. Mesoscopic eigenvalue statistics of Wigner matrices, with Antti Knowles. Annals of Applied Probability, 27 (2017), 1510-1550.

Other texts

  1. Lecture notes on Probability Limit Theory. These notes also clarify the discovery of integration by parts on the shift variable in the study of non-Hermitian random matrices, as well as the history of the use of cumulant expansion.
  2. Random matrix theory: local laws and applications, with Zhigang Bao and Fan Yang. Handbook of Statistics, 51 (2024), Chapter 12, 143–173.
  3. Bulk eigenvalue fluctuations of sparse Erdős–Rényi graphs. Oberwolfach reports, 16 (2019), 3489-3490.