平均场耦合映射的混沌传播与高斯波动
Propagation of Chaos and Gaussian Fluctuations for Mean-field Coupled Maps
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中文总结 AI 辅助
该研究针对平均场耦合映射对应的离散时间相互作用粒子系统，建立了相关估计与CLT型结果，证明混沌传播及经验测度波动依分布收敛于高斯过程，兼具定性与定量结论。
中文摘要 AI 辅助
我们研究一类源自平均场耦合映射的离散时间相互作用粒子系统。针对这类系统，我们建立了Dobrushin型估计、相对熵估计以及中心极限定理（CLT）型结果。首先，我们控制经验测度与极限分布之间的1-瓦瑟斯坦距离的增长；接着，利用相对熵方法证明混沌传播；最后，考虑经验测度波动的渐近行为，证明波动过程序列依分布收敛于某高斯过程，并建立了定性与定量结果。
英文摘要
We study a class of discrete-time interacting particle systems arising from mean-field coupled maps. We establish a Dobrushin-type estimate, a relative entropy estimate and Central Limit Theorem (CLT) type results for this class of systems. First we control the growth of the 1-Wasserstein distance between the empirical measures and the limiting distributions. Then we use the relative entropy method to show the propagation of chaos. Finally we consider the asymptotic behavior of the fluctuations for the empirical measures and prove that the sequence of fluctuation processes converges in distribution to some Gaussian process, where we establish both qualitative and quantitative results.
