Detalles de Evento
Título: Mean-field limit of particle systems over hypergraphs.
Conferenciante: Nastassia Pouradier Duteil (Sorbonne Université, Paris).
Resumen:
We present a generalization of non-exchangeable particle systems with higher-order interactions, by removing two important assumptions that are usually made in particle systems: that of exchangeability of particles, and that of superposition of binary interactions. In the general model that we consider, individuals instead interact by groups, so that a full group jointly generates a non-linear force on any individual. This interaction is modeled by an underlying hypergraph. We derive the mean-field limit of the particle system (i.e. its limit as the number of particles tends to infinity), and show that it is determined by a Vlasov-type equation, where the limit of the hypergraph is given by a so-called _unbounded-rank hypergraphon_, and the mean-field force admits infinitely-many orders of interactions. This work is in collaboration with N. Ayi (Sorbonne University) and D. Poyato (Universidad de Granada).
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