直至 Newton 奇性的多物种中等相互作用粒子系统的混沌传播
Propagation of chaos for multi-species moderately interacting particle systems up to Newtonian singularity
AI总结：
本文用相对熵与停时方法，证明多物种中等相互作用粒子系统在无粒子级截断下可逼近直至 Newton/Coulomb 奇性的聚集–扩散系统，并给出定量 L^1 收敛速率。
摘要：
我们通过具有定量界的相对熵方法，从随机相互作用粒子系统导出一类多物种聚集–扩散系统。我们利用中等相互作用粒子系统逼近吸引/排斥奇异势（直至 Newton/Coulomb 奇性，且在粒子层面不引入额外截断），证明了一个代数阶的 L^1 收敛结果。第一步是利用粒子系统联合分布与一个近似的极限聚集–扩散系统之间的相对熵。证明中的一个关键论证是通过停时论证证明依概率收敛。第二步是从近似 PDE 系统获得趋向极限聚集–扩散系统的定量收敛速率；这是通过估计相对熵与 L^2 距离的组合来证明的。
英文摘要：
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.
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