Entropic propagation of chaos for mean field diffusion with $L^p$ interactions via hierarchy, linear growth and fractional noise

Understand

New quantitative propagation of chaos results for mean field diffusion are proved via local and global entropy estimates.

• In the first result we work on the torus and consider singular, divergence free interactions $K\in L^p$, $p>d$.
• We prove a $O(k^{2}/n^2)$ convergence rate in relative entropy between the $k$-marginal laws of the particle system and its limiting law at each time $t$, as long as the same holds at time 0.
• The proof is based on local estimates via a form of BBGKY hierarchy and exemplifies a method to extend the framework in Lacker [16] to singular interactions.