I am interested in probability theory and its applications to problems from statistical physics, combinatorics, 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.
- interacting particle systems, e.g. discrete log gas, nonintersecting random walks and tilings, proving the universality of their asymptotic behaviors.
- statistical learning, investigating optimization and generalization properties.

*Large Deviations Asymptotics of Rectangular Spherical Integral*

with Alice Guionnet.

Preprint, 2021.*Spectrum of Random d-regular Graphs Up to the Edge*

with Horng-Tzer Yau.

Preprint, 2021.- Invertibility of adjacency matrices for random d-regular graphs

Accepted by Duke Mathematical Journal, 2021. *Large Deviation Principles via Spherical Integrals*

with Serban Belinschi and Alice Guionnet.

Preprint, 2020.*Edge rigidity and universality of random regular graphs of intermediate degree*

with Roland Bauerschmidt, Antti Knowles and Horng-Tzer Yau.

Geometric and Functional Analysis, 30(3):693--769, 2020.*Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős–Rényi graphs*.

with Benjamin Landon and Horng-Tzer Yau.

Annals of Probability, 48(2):916--962, 2020.*Spectral Statistics of Sparse Erdős–Rényi Graph Laplacians*

with Benjamin Landon.

Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, volume 56, pages 120--154, 2020.*Eigenvalues for the Minors of Wigner Matrices*

Preprint, 2019.*Local Kesten--McKay Law for Random Regular Graphs*

with Roland Bauerschmidt and Horng-Tzer Yau.

Communications in Mathematical Physics, 369(2):523--636, 2019.- Invertibility of adjacency matrices for random d-regular directed graphs,

Permanent draft, 2018. *Eigenvector Statistics of Sparse Random Matrices*

with Paul Bourgade and Horng-Tzer Yau.

Electron. J. Probab. Volume 22 (2017), paper no. 64, 38 pp.*Bulk Eigenvalue Statistics for Random Regular Graphs*

with Roland Bauerschmidt, Antti Knowles and Horng-Tzer Yau.

Ann. Probab., Volume 45, no. 6A (2017), 3626-3663.*Bulk Universality of Sparse Random Matrices*

with Benjamin Landon and Horng-Tzer Yau.

J. Math. Phys. 56 (2015), no. 12, 123301, 19pp.

*Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble*

with Amol Aggarwal.

Preprint, 2021.*Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains*

Preprint, 2021.*Law of Large Numbers and Central Limit Theorems by Jack Generating Functions*

Advances in Mathematics 380, 107545, 2021.*β-Nonintersecting Poisson Random Walks: Law of Large Numbers and Central Limit Theorems*

International Mathematics Research Notices, 2021(8), 5898-5942.*Edge Universality for Nonintersecting Brownian Bridges*

Preprint, 2020.*Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks*

Preprint, 2020.*Dyson Brownian Motion for General β and Potential at the Edge*

with Arka Adhikari.

Probability Theory and Related Fields, 178, 893–950, 2020.*Rigidity and Edge Universality of Discrete β-Ensembles*

with Alice Guionnet.

Communications on Pure and Applied Mathematics, 72(9):1875--1982, 2019.*Local Law and Mesoscopic Fluctuations of Dyson Brownian Motion for General β and Potentials*

with Benjamin Landon.

Probability Theory and Related Fields, 175(1-2):209--253, 2019.

*Improve Unscented Kalman Inversion With Low-Rank Approximation and Reduced-Order Model*

with Daniel Z Huang.

preprint, 2021.*Unscented Kalman Inversion: Efficient Gaussian Approximation to the Posterior Distribution*

with Daniel Z Huang.

preprint, 2021.*Power Iteration for Tensor PCA*

with Guang Cheng, Daniel Z. Huang and Qing Yang.

preprint, 2020.*Towards Understanding the Dynamics of the First-Order Adversaries*

with Zhun Deng, Hangfeng He and Weijie Su.

In Proceedings of the 37th International Conference on Machine Learning(ICML), 2020.*Dynamics of deep neural networks and neural tangent hierarchy*

with Horng-Tzer Yau.

In Proceedings of the 37th International Conference on Machine Learning(ICML), 2020.*Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes*

with Kenji Kawaguchi.

In Proceedings of the 57th Allerton Conference on Communication, Control, and Computing (Allerton), IEEE, 2019.*Every Local Minimum Value is the Global Minimum Value of Induced Model in Non-convex Machine Learning*

with Kenji Kawaguchi and Leslie Pack Kaelbling.

Neural Computation, 31(12), 2293-2323, MIT press, 2019.*Effect of Depth and Width on Local Minima in Deep Learning*

with Kenji Kawaguchi and Leslie Pack Kaelbling.

Neural Computation, 31(7), 1462-1498, MIT press, 2019.

*Mesoscopic Perturbations of Large Random Matrices*

Random Matrices Theory Appl., Volume 07, no. 02, 1850004 (2018).*Asymptotic Expansion of Spherical Integral*

J. Theor. Probab., (2018).*Laurent Phenomenon Sequences*

with Joshua Alman and Cesar Cuenca.

J. Algebraic Combin. 43 (2016), no. 3 589-633.