My main research interests include probabilistic combinatorics, random structures, random matrix theory and its applications.
Google Scholar, orcid.org/0000-0001-8128-3441
- Symmetric radial decreasing rearrangement can increase the fractional Gagliardo norm in domains, (with D. Li), to appear in Communications in Contemporary Mathematics. pdf
- Random perturbation and matrix sparsification and completion, (with S. O’Rourke, V. Vu), submitted. arXiv link.
- A generalized Hardy-Ramanujan formula for the number of restricted integer partitions (with T. Jiang), submitted. arXiv link. pdf
- Limiting empirical spectral distribution for the non-backtracking matrix of an Erdos-Renyi random graph (with P. M. Wood), submitted. arXiv link. pdf
Random restricted partitions (with T. Jiang), preprint. arXiv link. pdf
Eigenvectors of random matrices: a survey (with S. O’Rourke and V. Vu), Journal of Combinatorial Theory, Series A, 144:361–442 (2016). arXiv link. pdf
Statistical properties of eigenvalues of Laplace-Beltrami operators (with T. Jiang), submitted. arXiv link. pdf
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 link. pdf
Random weighted projections, random quadratic forms and random eigenvectors (with V. Vu), Random Struct. Alg., 47(4): 792–821 (2015). arXiv link. pdf
New methods for handling singular covariance matrices (with G. Tucci), submitted. arXiv link. pdf
Random covariance matrices: Universality of local statistics of eigenvalues up to the edge, Random Matrices: Theory and Appl. 1 (2012). arXiv link. pdf
Sparse random graphs: Eigenvalues and Eigenvectors (with L. Tran and V. Vu), Random Struct. Alg., 42(1):110–134 (2013). arXiv link. pdf
- An Innovative Approach for Analyzing Rank Deficient Covariance Matrices (With G. Tucci), Proceeding of the International Symposium on Information Theory, Boston, 2012. Link: Proceeding.