论文标题
具有奇异吸引人内核的平均场极限和定量估计值
Mean-field limit and quantitative estimates with singular attractive kernels
论文作者
论文摘要
本文证明了许多粒子之间具有奇异吸引人相互作用的许多粒子系统的平均场限制和定量估计值。作为一个重要的例子，首次获得了最佳亚临界方案中Patlak-Keller-Segel模型的完全严格推导（具有定量估计）。为了解决这个长期存在的问题，我们利用了新的调制自由能，并证明了一些精确的大偏差估计值，编码扩散和吸引力之间的竞争。结合已经在s {é} Minaire Laurent Schwartz进行的对抗核的范围[https://slsedp.centre-mersenne.org/journals/slsedp/]，我们提供了[C. R. Acad。科学部分数学（2019）]。
This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the Patlak-Keller-Segel model in optimal subcritical regimes is obtained for the first time. To give an answer to this longstanding problem, we take advantage of a new modulated free energy and we prove some precise large deviation estimates encoding the competition between diffusion and attraction. Combined with the range of repulsive kernels, already treated in the s{é}minaire Laurent Schwartz proceeding [https://slsedp.centre-mersenne.org/journals/SLSEDP/ ], we provide the full proof of results announced by the authors in [C. R. Acad. Sciences Section Maths (2019)].
