Mercoledì *5 febbraio *alle ore *14.30, *Simone Baldassarri (Mathematical Institute Leiden University) terrà il seminario dal titolo “*Opinion dynamics on dense dynamic random graphs*”. Abstract: Describing the evolution of dynamic networks together with dynamic processes running on them constitutes a major challenge in network science. Despite considerable efforts in past years, and notable progress on an intuitive and approximative level, our mathematical understanding of such systems is still in its infancy. The focus of this talk will be two-opinion voter models on dense dynamic random graphs. The goal is to understand and describe the occurrence of consensus versus polarisation over long periods of time. The former means that all vertices have the same opinion, the latter means that the vertices split into two communities with different opinions and few disagreeing edges. We consider three models for the joint dynamics of opinions and graphs: one with one-way feedback and two with two-way feedback. In the first model only coexistence is attainable, meaning that both opinions survive, but with the presence of many disagreeing edges. In the second model only consensus prevails, while in the third model polarisation is possible. Key results cover functional laws of large numbers for the densities of the two opinions, functional laws of large numbers for the dynamic random graphs in the space of graphons, and a characterisation of the limiting densities in terms of Beta-distributions.
Il seminario avrà luogo in presenza presso il Dipartimento di Matematica e Fisica di Roma Tre Aula B in Via della Vasca Navale 84, 00146 Roma