基于Glivenko-Cantelli的Hölder连续相互作用核的混沌传播
Propagation of chaos for Hölder continuous interaction kernels via Glivenko-Cantelli
摘要：
我们开发了一种新的技术，用于建立相互作用粒子系统的混沌定量传播。使用这种技术，我们证明了扩散粒子的相互作用内核仅仅是赫尔德连续的混沌传播，即使在很长的范围。此外，我们不需要特别准备的初始数据。同时，我们建立了一类向量场上随机微分方程的大数定律。证明汇集了来自经验过程理论和随机流的思想。
英文摘要：
We develop a new technique for establishing quantitative propagation of chaos for systems of interacting particles. Using this technique we prove propagation of chaos for diffusing particles whose interaction kernel is merely Hölder continuous, even at long ranges. Moreover, we do not require specially prepared initial data. On the way, we establish a law of large numbers for SDEs that holds over a class of vector fields simultaneously. The proofs bring together ideas from empirical process theory and stochastic flows.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
