Research

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• Journals:

1. Analysis of singular subspaces under random perturbations, submitted.  
2. (With S. O’Rourke, V. Vu) Matrices with Gaussian noise: optimal estimates for singular subspace perturbation, IEEE Transactions on Information Theory, 70(3):1978–2002 (2024).  
3. (With P. M. Wood) Limiting empirical spectral distribution for the non-backtracking matrix of an Erdos-Rényi random graph, Combinatorics, Probability and Computing, 1-18 (2023).  
4. (With T. Jiang) Asymptotic Properties of Random Restricted Partitions, Mathematics, 11(2), 417 (2023). (Special Issue "Random Combinatorial Structures".)  
5. (With Z. Bao, X. Ding, J. Wang) Statistical inference for principal components of spiked covariance matrices, Ann. Statist. 50(2) 1144-1169 (2022).  
   - Note: This paper overlaps and greatly extends a previous draft that can be found at arXiv:1907.12251.
6. (with J.-F. Cai, D. Li and J. Sun) Enhanced expressive power and fast training of neural networks by random projections, CSIAM Trans. Appl. Math., 2 (2021), pp. 532-550.  
7. (With T. Jiang) Statistical properties of eigenvalues of Laplace-Beltrami operators, Journal of Theoretical Probability (2021).  
8. (With Z. Bao, X. Ding) Singular vector and singular subspace distribution for the matrix denoising model, Ann. Statist. 49 (1) 370 - 392 (2021).  
9. (With T. Jiang) A generalized Hardy-Ramanujan formula for the number of restricted integer partitions, Journal of Number Theory, Volume 201, Pages 322-353 (2019).  
10. (With L. Guan, D. Li, K. Zhao) On a Class of Nonlocal SIR Models, Journal of Mathematical Biology, 78(6): 1581–1604 (2019).
11. (With D. Li) Symmetric radial decreasing rearrangement can increase the fractional Gagliardo norm in domains, Communications in Contemporary Mathematics, Vol. 21, No. 07, 1850059 (2019).
12. (With G. Tucci) New methods for handling singular covariance matrices, IEEE Transactions on Information Theory, 65(2): 770–786 (2019).
13. (With S. O’Rourke, V. Vu) Random perturbation of low rank matrices: Improving classical bounds, Linear Algebra and its Applications, 540:26-59 (2018).  
14. (With S. O’Rourke, V. Vu) Eigenvectors of random matrices: a survey, Journal of Combinatorial Theory, Series A, 144:361-442 (2016).  
15. (With V. Vu) Random weighted projections, random quadratic forms and random eigenvectors, Random Structures & Algorithms, 47(4): 792-821 (2015).  
16. (With L. Tran, V. Vu) Sparse random graphs: Eigenvalues and eigenvectors, Random Structures & Algorithms, 42(1): 110-134 (2013).  
17. Random covariance matrices: Universality of local statistics of eigenvalues up to the edge, Random matrices: Theory and Applications 1.01 (2012).  

• Conferences:

1. (With S. O’Rourke, V. Vu) Optimal Subspace Perturbation Bounds under Gaussian Noise, IEEE International Symposium on Information Theory - Proceedings, 2023, article number 10206931, p. 2601-2606.
2. (With G. Tucci) An Innovative Approach for Analysing Rank Deficient Covariance Matrices, IEEE International Symposium on Information Theory - Proceedings, 2012, article number 6283987, p. 2596-2600.