# Fei Cao

Visiting Assistant Professor

My research focuses on various interacting particle systems linking stochastic N-particle system and partial differential equations. The main challenge involved in the investigation of many interacting particle systems is to connect two levels of description of these systems: a microscopic description (particle dynamics) and a macroscopic description (PDEs). One of the many questions addressed by particle systems arising in physical, social, and life sciences is to understand how local interactions among individuals/particles lead to the formation of large structures. The derivation and analysis of macroscopic models give new insights to understand these phenomena. My research can be divided into two main axis:

- derivation of macroscopic models from microscopic dynamics,
- numerical and analytically study of the macroscopic models obtained.

On the other hand, I also embrace any opportunity to work in areas closely related to interacting particle systems, for instance the mathematics of the theoretic machine/deep learning. My primary interests in the growing field of machine/deep learning are the mathematical mechanism behind the (stochastic) gradient descent related algorithms used in classification and/or regression tasks, but I am also willing to get my feet wet on other topics in theoretic computer science.

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Education

Ph.D in Applied Mathematics, Arizona State University, USA (2017 - 2022)

Bachelor in Applied Mathematics, Southwestern University of Finance and Economics, China (2013 - 2017)

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Research Interests

Interacting particle system, Partial differential equations, Theoretical computer science

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Selected Publications

1. F. Cao, S. Motsch, A. Reamy, R. Theisen, Asymptotic flocking for the three-zone model, Mathematical Biosciences and Engineering, AIMS Press, 17 (6) (2020) 7692-7707.

2. F. Cao, K-averaging agent-based model: propagation of chaos and convergence to equilibrium, Journal of Statistical Physics, Springer, 184 (2) (2021) 1-19.

3. F. Cao, Explicit decay rate for the Gini index in the repeated averaging model, Mathematical Methods in the Applied Sciences, (2022) 1-14.

4. F. Cao, S. Motsch, Derivation of wealth distributions from biased exchange of money, to appear on Kinetic & Related Models, (2023).

5. F. Cao, P-E. Jabin, S.Motsch, Entropy dissipation and propagation of chaos for the uniform reshuffling model, to appear on Mathematical Models and Methods in Applied Sciences, (2023)

6. F. Cao, S.Motsch, Uncovering a two-phase dynamics from a dollar exchange model with bank and debt, arXiv preprint arXiv:2208.11003.

7. F. Cao, P-E. Jabin, From interacting agents to Boltzmann-Gibbs distribution of money, arXiv preprint arXiv:2208.05629.

8. F. Cao, R. Cortez, Uniform propagation of chaos for a dollar exchange econophysics model, arXiv preprint arXiv:2212.08289.

9. F. Cao, N. Marshall, From the binomial reshuffling model to Poisson distribution of money, arXiv preprint arXiv:2212.14388.