# Mean-field and graph limits for collective dynamics models with time-varying weights

### Nathalie Ayi – Jacques-Louis Lions Laboratory, Sorbonne University, France

In this work, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions’ evolution. We explore the natural question of the large population limit with two approaches: the now classical mean-field limit and the more recent graph limit. After establishing the existence and uniqueness of solutions to the models that we will consider, we provide a rigorous mathematical justification for taking the graph limit in a general context. Then, establishing the key notion of indistinguishability, which is a necessary framework to consider the mean-field limit, we prove the subordination of the mean-field limit to the graph one in that context. This actually provides an alternative (but weaker) proof for the mean-field limit. We conclude by showing some numerical simulations to illustrate our results.

Bio: Nathalie Ayi is an Assistant Professor at the Jacques Louis Lions laboratory at Sorbonne University (Paris). Before joining this laboratory, she was a post-doctoral fellow in the IPSO INRIA team at Rennes. She received her PhD degree in Mathematics from the University of Nice Sophia-Antipolis in 2016. Her field of research is partial differential equations with a specific interest in kinetic theory and the study of scaling limits.

### Location

Montréal Québec

Canada