What is it that drives some people to do mathematics in the pursuit of knowledge so abstract it can be communicated to but a small group of people? The only answer I can give employs two words: mathematics is beautiful, and it is true.

— James Simons, Renaissance Technologies

My current research interests are (1) exchangeable structures, Bayesian nonparametric statistics, and machine learning (2) Coulomb gases and related dependent point processes (3) heavy-tailed random matrices. Below is a list of all of my research papers sorted by topic. They are not necessarily in chronological order.

Bayesian Statistics and Neural Networks

  • “Deep neural networks with dependent weights: Gaussian Process mixture limit, heavy tails, sparsity and compressibility”
    Submitted (arXiv:2205.08187)
    with Fadhel Ayed, François Caron, Hoil lee, Juho Lee, and Hongseok Yang.
  • \alpha-Stable convergence of heavy-tailed infinitely-wide neural networks”
    Submitted (arXiv:2106.11064)
    with Hoil Lee, Jiho Lee, and Hongseok Yang.
  • “A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs”
    Annales Henri Lebesgue (2021) 4:325-368
    with Jiho Lee, Sam Staton, and Hongseok Yang.
    Honorable mention poster, 12th International Conference on Bayesian Nonparametrics.

Coulomb Gases

Random Matrices

Chaotic Billiards

  • “Necessary and sufficient condition for \mathcal{M}_2-convergence to a Lévy process for billiards with cusps at flat points”
    Stochastics and Dynamics (to appear) (arXiv:1902.08958)
    with Ian Melbourne, Françoise Pène, Paulo Varandas, and Hongkun Zhang.
  • “Convergence to stable Lévy motion for chaotic billiards with several cusps at flat points”
    Nonlinearity, (2019) 33:807-839
    with Françoise Pène and Hongkun Zhang.
  • “Stable Laws for Chaotic Billiards with Cusps at Flat Points”
    Annales Henri Poincaré, (2018) 19:3815-3853
    with Hongkun Zhang.

Stable Processes/Fractional Brownian Motion

Interacting Particle Systems