Renjie Feng

 

Postdoctoral research fellow in the School of Mathmatics and Statistics and Sydney Mathematical Research Institute at the University of Sydney, supervised by Prof. Geordie Williamson. I got Ph.D. from Northwestern University under the supervision of Steve Zelditch.

My academic profile at the Faculty of Science of the University of Sydney.

My personal homepage at Google Sites and GitHub.

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

Email: renjie.feng@sydney.edu.au

Research Interests

I am a member of the Pure Mathematics research group, within the subgroup Geometry, Topology and Analysis.

My reseach covers various areas in analysis, including probability theory, geometry and their intersection, especially random matrices and random geometry.

Publications

The links for all papers are available at my Google Scholar. A summary of my key research findings can be found at my Google Sites.

Random matrices
  1. Small gaps for GSE (with J. Li and D. Yao)
    near completion, available upon request.
  2. Determinantal point processes on spheres: multivariate linear statistics (with F. Götze and D. Yao)
    arXiv:2301.09216, submitted to Annals of Probability.
  3. Principal minors of GOE (with G. Tian, D. Wei, and D. Yao)
    arXiv:2205.05732, submitted to Transactions of the AMS.
  4. Large gaps of CUE and GUE (with D. Wei)
    submitted to Annals of Probability.
  5. Normality of circular β-ensemble (with G. Tian and D. Wei)
    Annals of Applied Probability, 33(6B): 5050-5070 (2023).
  6. Small gaps of circular β-ensemble (with D. Wei)
    Annals of Probability, 49(2): 997-1032 (2021).
  7. Small gaps of GOE (with G. Tian and D. Wei)
    GAFA, 29 (2019), no. 6, 1794-1827.
  8. Spectrum of SYK model (with G. Tian and D. Wei)
    Peking Mathematical Journal, 2, 41-70 (2019).
  9. Spectrum of SYK model II: Central limit theorem (with G. Tian and D. Wei)
    Random Matrices: Theory and Applications, 10(04), 2150037 (2021).
  10. 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).
    11. Random geometry
  11. Smallest distances between zeros of Gaussian analytic functions (with D. Yao)
    submitted to Annals of Probability, 2023.
  12. Smallest gaps between zeros of stationary Gaussian processes (with D. Yao and F. Götze)
    accepted for publication at Journal of Functional Analysis, 2024.
  13. Critical radius and supermum of random waves over Riemannian manifolds (with D.Yao and R.Adler)
    near completion, available upon request.
  14. Zeros of repeated derivatives of random polynomials (with D. Yao)
    Analysis & PDE, 12(6), 1489-1512, 2019.
  15. Critical radius and supremum of random spherical harmonics (with R. Adler)
    Annals of Probability, 47(2), 1162-1184 (2019).
  16. Correlations between zeros and critical points of random analytic functions
    Transactions of the AMS, 371(8), 5247-5265 (2019).
  17. 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).
  18. Conditional expectations of random holomorphic fields on Riemann surfaces
    International Mathematics Research Notices, 2017(14), 4406-4434.
  19. 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.
  20. Critical values of random analytic functions on complex manifolds (with S. Zelditch)
    Indiana University Mathematics Journal, 63(3), 651-686 (2014).
  21. 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.
  22. Median and mean of the Supremum of L2 normalized random holomorphic fields (with S. Zelditch)
    Journal of Functional Analysis, 266(8), 5085-5107 (2014).
  23. Random Riesz energies on compact Kähler manifolds (with S. Zelditch)
    Transactions of the AMS, 365(10), 5579-5604 (2013).
  24. Large deviations for zeros of P(φ)_2 random polynomials (with S. Zelditch)
    Journal of Statistical Physics, 143, 619-635 (2011).
    25. Complex geometry and PDEs
  25. 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).
  26. 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).

  27. Szasz analytic functions and noncompact Kähler toric manifolds
    Journal of Geometric Analysis, 22 (1), 107-131 (2012).
  28. Periodic solutions of Abreu's equation (with G. Szekelyhidi)
    Mathematical Research Letters, 18(6), 1271-1279 (2011).

Recent Seminar and Conference Talks