Propagation of chaos and large deviations in mean-field models with jumps on block-structured networks

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.