"A mean-field approximation for network-based opinion dynamics"Jankowiak, GaspardWe consider a simple model for consensus of opinions, where individuals interact if they are connected, i.e. if they shared an edge of a graph, which is fixed in time. To study the asymptotic behavior in the limit of large time and large population, we develop a continuum description for these dynamics that captures the global dynamics when the number of individuals grows. The difficulty lies on the network of connections being described through the labelling of the individuals: this is not amenable to standard large-particle limits. We overcome this difficulty by introducing an evolving label-free network description. Some analytical results are derived, and this continuum model is compared to the original, agent based model by means of numerical simulations on various types of social networks. We focus in particular on the impact of homophily, which in this case is understood as the degree to which groups in the network are represented in the initial opinion distribution. This is a joint work with Gianluca Favre, Sara Merino and Lara Trussardi. |
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