Research Interests

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.

Research Papers

Sparse Random Graphs

  • 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). to appear in Ann. Probab., 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.

Interacting Particle Systems

  • β-Nonintersecting Poisson Random Walks: Law of Large Numbers and Central Limit Theorems, (2017). arXiv: 1708.07115.
  • Rigidity and Edge Universality of Discrete β-Ensembles, with Alice Guionnet, (2017). arXiv: 1705.05527.
  • Local Law and Mesoscopic Fluctuations of Dyson Brownian Motion for General β and Potentials, with Benjamin Landon, (2016). arXiv: 1612.06306.

Undergraduate Research

  • Mesoscopic Perturbations of Large Random Matrices, (2014). to appear in Random Matrices Theory Appl., arXiv: 1412.4193.
  • Asymptotic Expansion of Spherical Integral, (2013). to appear in J. Theoret. Probab., arXiv: 1309.1967.
  • Laurent Phenomenon Sequences, with Joshua Alman and Cesar Cuenca. J. Algebraic Combin. 43 (2016), no. 3 589-633. arXiv: 1309.0751.