论文标题
兰格文动力学的全球订单依赖性力和混乱的时间传播中的均匀性
Global contractivity for Langevin dynamics with distribution-dependent forces and uniform in time propagation of chaos
论文作者
论文摘要
我们研究了经典的二阶Langevin动力学和McKean-Vlasov类型的非线性二阶Langevin动力学的长期行为。通过耦合方法，我们在$ l^1 $ wasserstein距离中建立了全球收缩，对成对弱相互作用的尺寸无尺寸。对于对应于$κ$ strongly凸电势的外力，在某些情况下，获得了$ \ mathcal {o}（\sqrtκ）$的收缩率。但是收缩结果不仅限于这些力。它包括多孔电势和非级别型外力以及非毕业生型排斥和有吸引力的相互作用力。证明是基于新的距离函数，该距离功能结合了大小距离的两个收缩结果，并使用调整到距离的耦合方法。通过应用耦合的综合性适应，我们为相应的平均场粒子系统的混乱边界的时间传播均匀。
We study the long-time behaviour of both the classical second-order Langevin dynamics and the nonlinear second-order Langevin dynamics of McKean-Vlasov type. By a coupling approach, we establish global contraction in an $L^1$ Wasserstein distance with an explicit dimension-free rate for pairwise weak interactions. For external forces corresponding to a $κ$-strongly convex potential, a contraction rate of order $\mathcal{O}(\sqrtκ)$ is obtained in certain cases. But the contraction result is not restricted to these forces. It rather includes multi-well potentials and non-gradient-type external forces as well as non-gradient-type repulsive and attractive interaction forces. The proof is based on a novel distance function which combines two contraction results for large and small distances and uses a coupling approach adjusted to the distance. By applying a componentwise adaptation of the coupling we provide uniform in time propagation of chaos bounds for the corresponding mean-field particle system.
