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
- 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.
Interacting Particle Systems
- 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.
Undergraduate Research
- 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.