Quantitative convergence in relative entropy for a moderately interacting particle system on Rd

This article shows how to combine the relative entropy method in [19, 2] and the regularized L2(Rd)-estimate in [28] to prove a strong propagation of chaos result for the viscous porous medium equation from a moderately interacting particle system in L∞(0,T;L1(Rd))-norm. In the moderate interacting setting, the interacting potential is a smoothed Dirac Delta distribution, however, current results regarding the relative entropy methods for singular potentials do not apply. The propagation of chaos result for the porous media equation holds on Rd for any dimension d≥1 and provides a quantitative result where the rate of convergence depends on the moderate scaling parameter and the dimension d≥1. Additionally, the presented method can be adapted for moderately interacting systems for which the convergence probability in [22, 23] holds – thus a propagation of chaos result in relative entropy can be obtained for kernels approximating Coulomb potentials.