Research Interests
I am interested in probability theory and its applications to problems from statistics, combinatorics, statistical physics and computer science.
So far I have done research on
- sparse random graphs and random matrices: studying the spectral properties of random regular graphs and Erdős–Rényi graphs.
- interacting particle systems, e.g. discrete log gas, nonintersecting random walks and random tiling models: proving the universality of their asymptotic behaviors.
- statistical learning and deep neural networks: investigating optimization and generalization properties.
- posterior sampling and diffusion models: for Bayesian inference, generative models and uncertainty quantification of large-scale inverse problems.
Research Papers
Sparse Random Graphs
- Gaussian Waves and Edge Eigenvectors of Random Regular Graphs
with Yukun He and Horng-Tzer Yau
Preprint, 2025.
- Extremal eigenvectors of sparse random matrices
Yukun He and Chen Wang
Preprint, 2025.
- Ramanujan Property and Edge Universality of Random Regular Graphs
with Theo McKenzie and Horng-Tzer Yau
Preprint, 2024.
- The Spectral Distribution of Random Graphs with Given Degree Sequences
with Shuyi Wang and Kevin Li.
Preprint, 2024.
- Optimal Eigenvalue Rigidity of Random Regular Graphs,
with Theo McKenzie and Horng-Tzer Yau
Permanent draft, 2024.
- Edge universality of random regular graphs of growing degrees
with Horng-Tzer Yau.
Preprint, 2023.
- Edge Universality of Sparse Random Matrices
with Horng-Tzer Yau.
Accepted by Annales de l'Institut Henri Poincar{\'e} 2024.
- Spectrum of Random d-regular Graphs Up to the Edge
with Horng-Tzer Yau.
Communications on Pure and Applied Mathematics, 77(3), 1635-1723, 2024.
- Invertibility of adjacency matrices for random d-regular graphs
Duke Mathematical Journal 170(18): 3977-4032, 2021.
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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.
- 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.
Random Matrices
- Fluctuations for Non-Hermitian Dynamics
with Paul Bourgade and Giorgio Cipolloni,
Preprint, 2024.
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Extremal Eigenvalues of Random Kernel Matrices with Polynomial Scaling
with David Kogan and Sagnik Nandy,
Accepted by Random Matrices: Theory and Applications, 2025.
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Fluctuation of the Largest Eigenvalue of a Kernel Matrix with application in Graphon-based Random Graphs
with Anirban Chatterjee,
Preprint, 2024.
- Large Deviation Principles via Spherical Integrals
with Serban Belinschi and Alice Guionnet.
Probability and Mathematical Physics 3, no.3, p:543-625, 2022.
- Eigenvalues for the Minors of Wigner Matrices
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 58(4), 2201-2215, 2022.
- Large Deviations Asymptotics of Rectangular Spherical Integral
with Alice Guionnet.
Journal of Functional Analysis 285 (11), 110-144, 2023.
Interacting Particle Systems
- A Convergence Framework For Airy_β Line Ensemble via Pole Evolution
with Lingfu Zhang.
Preprint, 2024.
- Strong Characterization for the Airy Line Ensemble
with Amol Aggarwal.
Preprint, 2023.
- Local Statistics and Concentration for Non-intersecting Brownian Bridges With Smooth Boundary Data
with Amol Aggarwal.
Communications in Mathematical Physics, 406, 70, 2025.
- Edge Rigidity of Dyson Brownian Motion with General Initial Data
with Amol Aggarwal.
Electronic Journal of Probability, 29: 1-62, 2024.
- Asymptotics of Generalized Bessel Functions and Weight Multiplicities via Large Deviations of Radial Dunkl Processes
with Colin McSwiggen.
Probability Theory and Related Fields, 190, 941–1006, 2024.
- Dynamical Loop Equation
with Vadim Gorin.
The Annals of Probability, 52(5), 1758-1863, 2024.
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Law of Large Numbers and Central Limit Theorems by Jack Generating Functions
Advances in Mathematics 380, 107545, 2021.
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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.
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Dyson Brownian Motion for General β and Potential at the Edge
with Arka Adhikari.
Probability Theory and Related Fields, 178, 893–950, 2020.
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Rigidity and Edge Universality of Discrete β-Ensembles
with Alice Guionnet.
Communications on Pure and Applied Mathematics, 72(9):1875--1982, 2019.
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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.
Random Tilings
- Asymptotics of Symmetric Polynomials: A Dynamical Point of View
with Alice Guionnet
Preprint, 2024.
- Pearcey universality at cusps of polygonal lozenge tiling
with Fan Yang and Lingfu Zhang.
Communications on Pure and Applied Mathematics, 77(9), 3708-3784, 2024.
- Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble
with Amol Aggarwal.
Accepted by Forum of Mathematics, Pi, 2024.
- Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains
Probability Theory and Related Fields, 1-149, 2023.
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Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks
Preprint, 2020.
Posterior Sampling and Diffusion Models
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Convergence Analysis of Probability Flow ODE for Score-based Generative Models
with Daniel Zhengyu Huang and Zhengjiang Lin.
preprint, 2025.
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Fisher-Rao Gradient Flow: Geodesic Convexity and Functional Inequalities
with José A Carrillo, Yifan Chen, Daniel Zhengyu Huang and Dongyi Wei.
Preprint, 2024.
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Convergence Analysis of Probability Flow ODE for Score-based Generative Models
with Daniel Zhengyu Huang and Zhengjiang Lin.
IEEE Transactions on Information Theory, 71, 6, 2025.
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Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flows
with Yifan Chen, Daniel Zhengu Huang, Sebastian Reich and Andrew M Stuart.
Inverse Problems, 40(12), 2024.
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Sampling via Gradient Flows in the Space of Probability Measures
with Yifan Chen, Daniel Zhengyu Huang, Sebastian Reich and Andrew M Stuart.
Preprint, 2023.
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Efficient derivative-free Bayesian inference for large-scale inverse problems
with Daniel Z Huang, Sebastian Reich and Andrew M Stuart.
Inverse Problems 38 no.12 p: 125006, 2022.
Statistical Learning
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On self-training of summary data with genetic applications
with Buxin Su, Jin Jin and Bingxin Zhao.
preprint, 2025.
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Local geometry of high-dimensional mixture models: Effective spectral theory and dynamical transitions
with Gerard Ben Arous, Reza Gheissari and Aukosh Jagannath.
preprint, 2025.
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High-dimensional SGD aligns with emerging outlier eigenspaces
with Gerard Ben Arous, Reza Gheissari and Aukosh Jagannath.
International Conference on Learning Representations (ICLR) Spotlight, 2024.
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How Does Information Bottleneck Help Deep Learning?
with Kenji Kawaguchi, Zhun Deng and Xu Ji.
International Conference on Machine Learning (ICML), 2023.
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PatchGT: Transformer over Non-trainable Clusters for Learning Graph Representations
with Han Gao, Xu Han, Jian-Xun Wang and Liping Liu.
In Learning on Graphs Conference, pp. 27-1. PMLR, 2022.
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Long Random Matrices and Tensor Unfolding
with Gerard Ben Arous and Daniel Z Huang.
Annals of Applied Probability 33 (6B), 5753-5780, 2023.
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Power Iteration for Tensor PCA
with Guang Cheng, Daniel Z. Huang and Qing Yang.
Journal of Machine Learning Research 23 (128), 1-47,2022.
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Robustness Implies Generalization via Data-Dependent Generalization Bounds
Kenji Kawaguchi, Zhun Deng and Kyle Luh.
International Conference on Machine Learning (ICML) Long Presentation, 2022.
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Understanding End-to-End Model-Based Reinforcement Learning Methods as Implicit Parameterization
with with Clement Gehring, Kenji Kawaguchi, and Leslie Pack Kaelbling.
Advances in Neural Information Processing Systems (NeurIPS), 2021.
Deep Neural Networks
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How Shrinking Gradient Noise Helps the Performance of Neural Networks
with Zhun Deng, and Kenji Kawaguchi.
IEEE International Conference on Big Data (Big Data), 1002-1007, 2021.
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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.
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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.
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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.
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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.