# Research

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 random structures with applications to network 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.

## Exchangeable Random Structures

• “A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs” Annales Henri Lebesgue (to appear) (arXiv:1812.06282)
with Jiho Lee, Sam Staton, and Hongseok Yang.
Honorable mention poster, 12th International Conference on Bayesian Nonparametrics.

## 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.