2020/12/16 by Nathalie Ayi, Ayi, Nathalie, Nastassia Pouradier Duteil +1 · 39 citations
Mathematics · Medicine · Physics and Astronomy · #Analysis of PDEs (math.AP) #Applied mathematics #Complex Network Analysis Techniques #Context (archaeology) #Discrete mathematics #FOS: Mathematics #Field (mathematics) #Graph #Limit (mathematics) #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Mean field theory #Opinion Dynamics and Social Influence #Physics #Pure mathematics #Quantum mechanics #Statistical physics #Subordination (linguistics) #Uniqueness #math.AP
paper · pdf · doi:10.48550/arxiv.2012.08807
published in arXiv (Cornell University) (Cornell University)
arxiv created 2020/12/16 · openalex publication_date 2020/12/16 · arxiv updated 2020/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
In this paper, we study a model for opinion dynamics where the influence\nweights of agents evolve in time via an equation which is coupled with the\nopinions' evolution. We explore the natural question of the large population\nlimit with two approaches: the now classical mean-field limit and the more\nrecent graph limit. After establishing the existence and uniqueness of\nsolutions to the models that we will consider, we provide a rigorous\nmathematical justification for taking the graph limit in a general context.\nThen, establishing the key notion of indistinguishability, which is a necessary\nframework to consider the mean-field limit, we prove the subordination of the\nmean-field limit to the graph one in that context. This actually provides an\nalternative (but weaker) proof for the mean-field limit. We conclude by showing\nsome numerical simulations to illustrate our results.\n