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 the late 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
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Email: |
renjie.feng@sydney.edu.au
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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
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Small gaps for GSE (with J. Li and D. Yao)
arXiv:2409.03324, submitted. -
Determinantal point processes on spheres: multivariate linear statistics (with F. Götze and D. Yao)
arXiv:2301.09216, under review at Annals of Probability.
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Principal minors of GOE (with G. Tian, D. Wei, and D. Yao)
arXiv:2205.05732, under review at Annals of Applied Probability.
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Large gaps of CUE and GUE (with D. Wei)
under reviw at Annals of Probability.
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The Berry-Esseen theorem for circular β-ensemble (with G. Tian and D. Wei)
Annals of Applied Probability, 33(6B): 5050-5070 (2023).
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Small gaps of circular β-ensemble (with D. Wei)
Annals of Probability, 49(2): 997-1032 (2021).
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Small gaps of GOE (with G. Tian and D. Wei)
GAFA, 29 (2019), no. 6, 1794-1827.
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Spectrum of SYK model (with G. Tian and D. Wei)
Peking Mathematical Journal, 2, 41-70 (2019).
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Spectrum of SYK model II: Central limit theorem (with G. Tian and D. Wei)
Random Matrices: Theory and Applications, 10(04), 2150037 (2021).
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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).
Random geometry
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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.
- Smallest distances between zeros of Gaussian analytic functions (with D. Yao)
under review at Advances in Mathematics, 2024.
- Critical radius and supermum of random waves over Riemannian manifolds (with D.Yao and R.Adler)
near completion, available upon request.
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Zeros of repeated derivatives of random polynomials (with D. Yao)
Analysis & PDE, 12(6), 1489-1512, 2019.
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Critical radius and supremum of random spherical harmonics (with R. Adler)
Annals of Probability, 47(2), 1162-1184 (2019).
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Correlations between zeros and critical points of random analytic functions
Transactions of the AMS, 371(8), 5247-5265 (2019).
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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).
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Conditional expectations of random holomorphic fields on Riemann surfaces
International Mathematics Research Notices, 2017(14), 4406-4434.
- 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.
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Critical values of random analytic functions on complex manifolds (with S. Zelditch)
Indiana University Mathematics Journal, 63(3), 651-686 (2014).
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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.
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Median and mean of the Supremum of L2 normalized random holomorphic fields
(with S. Zelditch)
Journal of Functional Analysis, 266(8), 5085-5107 (2014).
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Random Riesz energies on compact Kähler manifolds (with S. Zelditch)
Transactions of the AMS, 365(10), 5579-5604 (2013).
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Large deviations for zeros of P(φ)_2 random polynomials (with S. Zelditch)
Journal of Statistical Physics, 143, 619-635 (2011).
Complex geometry and PDEs
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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).
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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).
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Szasz analytic functions and noncompact Kähler toric manifolds
Journal of Geometric Analysis, 22 (1), 107-131 (2012).
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Periodic solutions of Abreu's equation (with G. Szekelyhidi)
Mathematical Research Letters, 18(6), 1271-1279 (2011).
Survey
- Extreme gap problems in random matrix theory
Surveys in Geometric Analysis Volume 3, 2019, 2024 - EDP Sciences.
Recent Seminar and Conference Talks
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A quick introduction to random matrices and extreme gap problems
The Australian National University, June, 2024.
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Determinantal point processes on spheres: Multivariate linear statistics
Stochastic processes seminar, The University of Melbourne, March, 2024.
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Extreme spacings for classical random matrices
Random matrix theory group seminar, The University of Melbourne, March, 2024.
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A graphical formula for cumulants of multivariate linear statistics of determinantal point processes
Probability and Mathematical Statistics, 67th Annual Meeting of the Australian Mathematical Society, Dec, 2023.
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Determinantal point processes on spheres: Multivariate linear statistics
Applied Maths Seminar, The University of Sydney, Oct, 2023.
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A quick introduction to random matrices and extreme gap problems
SMRI seminar, The University of Sydney, Sep, 2023.
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Determinantal point processes on the sphere
Research Seminar on Probability and Geometry, Ruhr-Universität Bochum, Germany, May, 2023.
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Determinantal point processes on spheres: Multivariate linear statistics
Seminar Bielefeld-Melbourne-Seoul Random Matrices (online), March, 2023.
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Determinantal point processes on spheres: Multivariate linear statistics
Institute of Applied Mathematics, Chinese Academy of Sciences, Feb, 2023.
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Extreme gap problems and the SYK model
Lille days on Point Processes and stochastic Geometry, Université de Lille, France, Oct, 2022.
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Extreme gap problems for classical random matrices
MPI-Oberseminar, Max Planck Institute for Mathematics, Germany, Aug, 2022.
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Extreme gaps for classical random matrices and the SYK model
Seminar Mathematical Physics, Bielefeld University, Germany, March, 2022.
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Extreme spacings of classical random matrices and the SYK model
Oberseminar Stochastics, University of Bonn, Germany, Jan, 2022.
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Random matrices and our recent results
MATH seminar, Bilkent University (online), March, 2021.
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Some recent results in random matrices
Institute of Applied Mathematics, Chinese Academy of Sciences, Oct, 2020.