I am interested in probability theory and its applications to problems from statistical physics, computer science and statistics. So far I have done research on sparse random graphs, studying the spectral properties of random regular graphs and Erdős–Rényi graphs. I have also worked on interacting particle systems, proving the universality of the known asymptotic behaviors.

*Invertibility of adjacency matrices for random d-regular graphs*, (2018). arXiv: 1807.06465.*Invertibility of adjacency matrices for random d-regular directed graphs*, (2018). arXiv: 1806.01382.*Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős–Rényi graphs*, with Benjamin Landon and Horng-Tzer Yau, (2017). arXiv: 1712.03936.*Local Kesten--McKay Law for Random Regular Graphs*, with Roland Bauerschmidt and Horng-Tzer Yau, (2016). arXiv: 1609.09052.*Eigenvector Statistics of Sparse Random Matrices*, with Paul Bourgade and Horng-Tzer Yau. Electron. J. Probab. Volume 22 (2017), paper no. 64, 38 pp. arXiv: 1609.09022.*Spectral Statistics of Sparse Erdős–Rényi Graph Laplacians*, with Benjamin Landon, (2015). to appear in Ann. Inst. H. Poincare Probab. Statist., arXiv: 1510.06390.*Bulk Eigenvalue Statistics for Random Regular Graphs*, with Roland Bauerschmidt, Antti Knowles and Horng-Tzer Yau, (2015). Ann. Probab., Volume 45, no. 6A (2017), 3626-3663. arXiv: 1505.06700.*Bulk Universality of Sparse Random Matrices*, with Benjamin Landon and Horng-Tzer Yau. J. Math. Phys. 56 (2015), no. 12, 123301, 19pp, arXiv: 1504.05170.

*Law of Large Numbers and Central Limit Theorems by Jack Generating Functions*, (2018). arXiv: 1807.09928.*β-Nonintersecting Poisson Random Walks: Law of Large Numbers and Central Limit Theorems*, (2017). to appear in Internat. Math. Res. Notices, arXiv: 1708.07115.*Rigidity and Edge Universality of Discrete β-Ensembles*, with Alice Guionnet, (2017). to appear in Comm. Pure Appl. Math., arXiv: 1705.05527.*Local Law and Mesoscopic Fluctuations of Dyson Brownian Motion for General β and Potentials*, with Benjamin Landon, (2016). to appear in Probab. Theory Relat. Fields, arXiv: 1612.06306.

*Mesoscopic Perturbations of Large Random Matrices*, Random Matrices Theory Appl., Volume 07, no. 02, 1850004 (2018). arXiv: 1412.4193.*Asymptotic Expansion of Spherical Integral*, J. Theor. Probab., (2018). arXiv: 1309.1967.*Laurent Phenomenon Sequences*, with Joshua Alman and Cesar Cuenca. J. Algebraic Combin. 43 (2016), no. 3 589-633. arXiv: 1309.0751.