论文标题
图形粒子系统的平稳性和均匀的时间收敛性
Stationarity and uniform in time convergence for the graphon particle system
论文作者
论文摘要
我们认为异质相互作用的扩散粒子系统及其较大的种群限制的长期行为。相互作用是平均场类型，其权重为基础图形。极限由图形粒子系统给出，该系统由独立但异质的非线性扩散组成，其概率分布完全耦合。在适当的假设（包括一定的凸条件）的合适假设下，我们显示了两个系统的指数成分，并随着粒子数量的增加，建立了边缘分布的统一定律，并引入了均匀的欧拉近似值。提供了欧拉近似的精确收敛速率。
We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by a graphon particle system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Under suitable assumptions, including a certain convexity condition, we show the exponential ergodicity for both systems, establish the uniform-in-time law of large numbers for marginal distributions as the number of particles increases, and introduce the uniform-in-time Euler approximation. The precise rate of convergence of the Euler approximation is provided.
