Author

Fuqing Gao

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Preprint Oct 2026

Hydrodynamic and Stochastic Limits of Space-Time Hawkes Processes

We study the large-scale behavior of critical and nearly critical space-time Hawkes processes initialized by a prescribed Poisson field of past events. The density of this initial field separates three macroscopic regimes. In the high-density regime, fluctuations average out and the event measure converges to a hydrody...

Fu-Qing Gao, Ying-Li Wang, Lin Zhu · 0 citations

Preprint Sep 2026

Villani's conjecture for Kac's walk

We prove Villani's conjecture on entropy production for Kac's walk with uniform collision angles. For every $N\geq2$, with total collision rate $N$, the optimal entropy production constant is $2/(N-1)$. We show that the known lower bound is sharp by constructing two families of smooth strictly positive probability dens...

Fuqing Gao, Shao-Chen Wang, Xian-Jie Xia · 0 citations