## Welcome

My name is Hoil Lee. I am a Ph.D. student in KAIST Dept of Mathematical Sciences. I study probability theory, and my advisor is Paul Jung.

**Research interests**

- Probability theory – Infinite and finite exchangeability, random graphs and graph limits (graphons).
- Statistical machine learning – Neural networks with heavy-tailed behavior.

**Publications**

- François Caron, Fadhel Ayed, Paul Jung,
**Hoil Lee**, Juho Lee, and Hongseok Yang,*“Over-parameterised Shallow Neural Networks with Asymmetrical Node Scaling: Global Convergence Guarantees and Feature Learning”*, submitted (arXiv:2302.01002). **Hoil Lee**, Fadhel Ayed, Paul Jung, Juho Lee, Hongseok Yang, and François Caron,*“Deep neural networks with dependent weights: Gaussian Process mixture limit, heavy tails, sparsity and compressibility”*, submitted (arXiv:2205.08187).- Paul Jung,
**Hoil Lee**, Jiho Lee, and Hongseok Yang,*“-Stable convergence of heavy-tailed infinitely-wide neural networks”*, to appear in Advances in Applied Probability, (arXiv:2106.11064).

**Talks**

*“-Stable convergence of heavy-tailed infinitely-wide neural networks”*, contributed talk, 2021 Korean Mathematical Society Annual meetings, October 2021, online.

**Academic travels**

*Random Matrices and Related Topics*, May 2019, KIAS, Seoul, Korea.*Conference in Honor of S. R. S. Varadhan’s 80th Birthday*, June 2022, Jeju, Korea.*New tools for optimal mixing of Markov chains: Spectral independence and entropy decay*, August 2022, UCSB, Santa Barbara, California.

**Solutions Manual to Durrett’s Probability: Theory and Examples, 5th edition**

Wonjun Seo, my dear freind in UC Davis statistics, and I are working on a project where we make solutions to every exercise problem in Durrett’s Probability: Theory and Examples, 5th edition. Here is the latest (incomplete) version of it. (Last updated on Sep. 9, 2021)