Propagation of chaos for multi-species moderately interacting particle systems up to Newtonian singularity

TL;DR

This paper establishes the propagation of chaos for multi-species particle systems with singular interactions up to Newtonian/Coulomb singularities, providing quantitative convergence bounds without particle-level cut-offs.

Contribution

It introduces a novel approach using relative entropy to prove convergence of multi-species systems with singular potentials up to Coulomb singularities, without additional regularization.

Findings

Proves algebraic L^1 convergence of particle systems to aggregation-diffusion limits.

Develops a stopping time argument for convergence in probability.

Provides explicit convergence rates from particle systems to PDE limits.

Abstract

We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting particle systems approximating attractive/repulsive singular potentials up to Newtonian/Coulomb singularities without additional cut-off on the particle level. The first step is to make use of the relative entropy between the joint distribution of the particle system and an approximated limiting aggregation-diffusion system. A crucial argument in the proof is to show convergence in probability by a stopping time argument. The second step is to obtain a quantitative convergence rate to the limiting aggregation-diffusion system from the approximated PDE system. This is shown by evaluating a combination of relative entropy and $L^2$-distance.