My main research interests include probabilistic combinatorics, random structures, random matrix theory and its applications.

Google Scholar, ORCID iD

Publications/Preprints (in reverse chronological order):

  1. Principal components of spiked covariance matrices in the supercritical regime, (with Zhigang Bao, Xiucai Ding and Jingming Wang), preprint. arXiv link.

  2. Enhanced expressive power and fast training of neural networks by random projections, (with Jian-Feng Cai, Dong Li and Jiaze Sun), submitted. arXiv link.
  3. Singular vector and singular subspace distribution for the matrix denoising model, (with Zhigang Bao and Xiucai Ding), submitted to Ann. Stat. arXiv link. pdf
  4. On a class of nonlocal SIR models, (With L. Guan, D. Li and K. Zhao),

    Journal of Mathematical Biology, Volume 78, Issue 6, pp 1581–1604 (2019). Journal linkpdf

  5. Symmetric radial decreasing rearrangement can increase the fractional Gagliardo norm in domains, (with D. Li), to appear in Communications in Contemporary Mathematics. Journal link. pdf
  6. Random perturbation and matrix sparsification and completion, (with S. O’Rourke, V. Vu), submitted. arXiv link.
  7. A generalized Hardy-Ramanujan formula for the number of restricted integer partitions (with T. Jiang), Journal of Number Theory, Volume 201, August 2019, Pages 322-353. arXiv linkpdf
  8. Limiting empirical spectral distribution for the non-backtracking matrix of an Erdos-Renyi random graph (with P. M. Wood), submittedarXiv linkpdf
  9. Random restricted partitions (with T. Jiang), preprint. arXiv link. pdf

  10. Eigenvectors of random matrices: a survey (with S. O’Rourke and V. Vu), Journal of Combinatorial Theory, Series A, 144:361–442 (2016). arXiv linkpdf

  11. Statistical properties of eigenvalues of Laplace-Beltrami operators (with T. Jiang), submittedarXiv linkpdf

  12. Random perturbation of low-rank matrices: Improving classical bounds (with S. O’Rourke and V. Vu), Linear Algebra and its Applications, 540:26–59 (2018)arXiv linkpdf

  13. Random weighted projections, random quadratic forms and random eigenvectors (with V. Vu), Random Struct. Alg., 47(4): 792–821 (2015). arXiv linkpdf

  14. New methods for handling singular covariance matrices (with G. Tucci), IEEE Transactions on Information Theory, 65(2): 770–786 (2019)arXiv linkpdf

  15. Random covariance matrices: Universality of local statistics of eigenvalues up to the edge, Random Matrices: Theory and Appl. 1 (2012). arXiv linkpdf

  16. Sparse random graphs: Eigenvalues and Eigenvectors (with L. Tran and V. Vu), Random Struct. Alg., 42(1):110–134 (2013). arXiv linkpdf

Conference Proceedings:

  1. An Innovative Approach for Analyzing Rank Deficient Covariance Matrices (With G. Tucci), Proceeding of the International Symposium on Information Theory, Boston, 2012. Link: Proceeding.