论文标题
混乱和大偏差在平均场模型中具有跳跃网络上跳跃的大偏差
Propagation of chaos and large deviations in mean-field models with jumps on block-structured networks
论文作者
论文摘要
分析了一种相互作用的多类有限状态跳跃过程的系统。所考虑的模型由具有动态变化多色节点的块结构网络组成。该相互作用是局部的，并通过局部经验措施进行了描述。考虑了两个级别的异质性：在节点被标记为两种类型的块之间和内部。中央节点仅连接到相同块的节点，而周围节点则连接到同一块的两个节点，并连接到其他块的一些节点。研究了粒子数量倾向于无穷大的系统的限制。在外围节点的规律性条件下，在多人群环境中建立了混乱和大量法律的传播。特别是，由于节点的数量流向无穷大，因此可以通过mckean-vlasov系统的解决方案来表示不同类别节点的行为。此外，我们证明了经验措施和经验过程的向量的大偏差原则。
A system of interacting multiclass finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-colors nodes. The interaction is local and described through local empirical measures. Two levels of heterogeneity are considered: between and within the blocks where the nodes are labeled into two types. The central nodes are those connected only to the nodes of the same block whereas the peripheral nodes are connected to both the nodes of the same block and to some nodes from other blocks. The limits of such systems as the number of particles tends to infinity are investigated. Under regularity conditions on the peripheral nodes, propagation of chaos and law of large numbers are established in a multi-population setting. In particular, it is shown that, as the number of nodes goes to infinity, the behavior of the different classes of nodes can be represented by the solution of a McKean-Vlasov system. Moreover, we prove large deviation principles for the vectors of empirical measures and the empirical processes.
