论文标题
图形子平均场系统
Graphon mean field systems
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人口限制。相互作用是平均场类型，其权重为基础图形。随着系统大小的增加和基础图形的收敛，建立了大量结果的定律。极限由图形均值场系统给出，该图形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。提供了此类系统的适应性，连续性和稳定性。我们还考虑了有限粒子系统的不太密集的类似物，该模拟是通过消失的速率和适当的相互作用缩放来获得的。证明了大量结果的定律，用于将这种系统与相应的图形平均场系统收敛。
We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as the system size increases and the underlying graphons converge. The limit is given by a graphon mean field system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Well-posedness, continuity and stability of such systems are provided. We also consider a not-so-dense analogue of the finite particle system, obtained by percolation with vanishing rates and suitable scaling of interactions. A law of large numbers result is proved for the convergence of such systems to the corresponding graphon mean field system.
