Renjie Feng

 

I am a Postdoctoral Research Fellow in Mathematics and AI at the School of Mathmatics and Statistics and Sydney Mathematical Research Institute at the University of Sydney, supervised by Prof. Geordie Williamson.

My academic profile at School of Mathematics and Statistics of the University of Sydney.

Address: Sydney Mathematical Research Institute L4.47
University of Sydney NSW 2006
Australia

Email: renjie.feng@sydney.edu.au

Research Interests

My research focuses on probability theory and its applications in machine learning and deep learning.

Publications

  1. Large gaps of CUE and GUE (with D. Wei)
    Annals of Probability, to appear, 2025+.
  2. Critical radii and suprema of random waves over Riemannian manifolds (with D. Yao and R. Adler)
    arXiv:2501.10798, submitted, 2025.
  3. Smallest gaps between zeros of stationary Gaussian processes (with D. Yao and F. Götze)
    Journal of Functional Analysis, Volume 287, Issue 4, 15 August 2024, 110493.
  4. Smallest distances between zeros of Gaussian analytic functions (with D. Yao)
    submitted, 2024.
  5. Small gaps for GSE (with J. Li and D. Yao)
    arXiv:2409.03324, submitted.
  6. Determinantal point processes on spheres: multivariate linear statistics (with F. Götze and D. Yao)
    arXiv:2301.09216, submitted.
  7. Principal minors of Gaussian orthogonal ensemble (with G. Tian, D. Wei, and D. Yao)
    arXiv:2205.05732, submitted.
  8. The Berry-Esseen theorem for circular β-ensemble (with G. Tian and D. Wei)
    Annals of Applied Probability, 33(6B): 5050-5070 (2023).
  9. Small gaps of circular β-ensemble (with D. Wei)
    Annals of Probability, 49(2): 997-1032 (2021).
  10. Small gaps of GOE (with G. Tian and D. Wei)
    GAFA, 29 (2019), no. 6, 1794-1827.
  11. Extreme gap problems in random matrix theory Surveys in Geometric Analysis, Volume 3 (2019), 19.
  12. Spectrum of SYK model (with G. Tian and D. Wei)
    Peking Mathematical Journal, 2, 41-70 (2019).
  13. Spectrum of SYK model II: Central limit theorem (with G. Tian and D. Wei)
    Random Matrices: Theory and Applications, 10(04), 2150037 (2021).
  14. Spectrum of SYK model III: Large deviations and concentration of measures (with G. Tian and D. Wei)
    Random Matrices: Theory and Applications, 09(02), 2050001 (2020).
  15. Zeros of repeated derivatives of random polynomials (with D. Yao)
    Analysis & PDE, 12(6), 1489-1512, 2019.
  16. Critical radius and supremum of random spherical harmonics (with R. Adler)
    Annals of Probability, 47(2), 1162-1184 (2019).
  17. Correlations between zeros and critical points of random analytic functions
    Transactions of the AMS, 371(8), 5247-5265 (2019).
  18. Critical radius and supremum of random spherical harmonics II (with X. Xu and R. Adler)
    Electronic Communications in Probability, 23, paper no. 50, 11 pp. (2018).
  19. Conditional expectations of random holomorphic fields on Riemann surfaces
    International Mathematics Research Notices, 2017(14), 4406-4434.
  20. Addendum to "Critical Values of Random Analytic Functions on Complex Manifolds" (with S. Zelditch)
    Indiana University Mathematics Journal, Vol. 66, No.1 (2017), pp. 23-29.
  21. Critical values of Gaussian SU(2) random polynomials (with Z. Wang)
    Proceedings of the American Mathematical Society, Vol. 144, No. 2 (February 2016), pp. 487-502.
  22. Critical values of random analytic functions on complex manifolds (with S. Zelditch)
    Indiana University Mathematics Journal, 63(3), 651-686 (2014).
  23. Median and mean of the Supremum of L2 normalized random holomorphic fields (with S. Zelditch)
    Journal of Functional Analysis, 266(8), 5085-5107 (2014).
  24. Random Riesz energies on compact Kähler manifolds (with S. Zelditch)
    Transactions of the AMS, 365(10), 5579-5604 (2013).
  25. Large deviations for zeros of P(φ)2 random polynomials (with S. Zelditch)
    Journal of Statistical Physics, 143, 619-635 (2011).
  26. Bergman metrics and geodesics in the space of Kähler metrics on principally polarized abelian varieties
    Journal of the Institute of Mathematics of Jussieu, 11(1), 1-25 (2012).
  27. The global existence and convergence of the Calabi flow on ℂn/ ℤn+iℤn (with H. Huang)
    Journal of Functional Analysis, 263(4), 1129-1146 (2012).
  28. Szasz analytic functions and noncompact Kähler toric manifolds
    Journal of Geometric Analysis, 22(1), 107-131 (2012).
  29. Periodic solutions of Abreu's equation (with G. Szekelyhidi)
    Mathematical Research Letters, 18(6), 1271-1279 (2011).
  30. Extreme gap problems in random matrix theory
    Surveys in Geometric Analysis, Volume 3, 2019 (2024): 19.
  31. Zeros and Critical Points of Random Fields
    PhD thesis, Northwestern University, 2012.

Seminar and Conference Talks since 2020