论文标题
混乱的尖锐统一传播
Sharp uniform-in-time propagation of chaos
论文作者
论文摘要
我们证明了混乱的定量传播的最佳速度，均匀地逐渐地进行了相互作用。我们的主要例子是由圆环上凸电势和模型与小相互作用的相互作用。我们表明，$ n $粒子系统的$ k $ - 粒子边缘及其限制产品度量为$ O（（k/n）^2）$，及时均匀地通过相对熵（相对熵），平方Quadratic Quadratic Quadratic wasserstein metric或Squared总变量来测量距离。我们的证明是基于通过BBGKY层次结构对相对熵的分析，通过Log-Sobolev的不平等，将第一作者的先前工作适应了时均匀的情况。
We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for interacting diffusions. Our main examples are interactions governed by convex potentials and models on the torus with small interactions. We show that the distance between the $k$-particle marginal of the $n$-particle system and its limiting product measure is $O((k/n)^2)$, uniformly in time, with distance measured either by relative entropy, squared quadratic Wasserstein metric, or squared total variation. Our proof is based on an analysis of relative entropy through the BBGKY hierarchy, adapting prior work of the first author to the time-uniform case by means of log-Sobolev inequalities.
