## 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.