We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution of all the other nodes and the edges connected to it, while the edge dynamics depends only on the corresponding nodes it connects. Asymptotic results, including law of large numbers, propagation of chaos, and central limit theorems, are established. In contrast to the classic McKean–Vlasov limit, the limiting system exhibits a path-dependent feature in that the evolution of a given particle depends on its own conditional distribution given its past trajectory. We also analyze the asymptotic behavior of the system when the edge dynamics is accelerated. A law of large number and a propagation of chaos result is established, and the limiting system is given as independent McKean–Vlasov processes. Error between the two limiting systems, with and without acceleration in edge dynamics, is also analyzed.

我们考虑具有动态变化的多色边的时变随机图上的弱相互作用跳跃过程。该系统由大量节点组成，其中节点动态取决于所有其他节点和与其相连的边的联合经验分布，而边动态仅取决于它所连接的相应节点。建立了渐近结果，包括大数定律、混沌传播和中心极限定理。与经典的 McKean-Vlasov 限制相反，限制系统表现出路径相关的特征，即给定粒子的演化取决于给定其过去轨迹的自身条件分布。我们还分析了边缘动力学加速时系统的渐近行为。建立了大数定律和混沌结果的传播，并将极限系统作为独立的 McKean-Vlasov 过程给出。两个限制系统之间的误差，有和没有边缘动力学加速，也被分析。