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A particle system is said to be non-exchangeable if two particles cannot beexchanged without modifying the overall dynamics. Because of this property, theclassical mean-field approach fails to provide a limit equation when the numberof particles tends to infinity. In this review, we present novel approaches forthe large-population limit of non-exchangeable particle systems, based on theidea of keeping track of the identities of the particles. These can beclassified in two categories. The non-exchangeable mean-field limit describesthe evolution of the particle density on the product space of particlepositions and labels. Instead, the continuum limit allows to obtain an equationfor the evolution of each particle's position as a function of its (continuous)label. We expose each of these approaches in the frameworks of static andadaptive networks.

Large-population limits of non-exchangeable particle systems