{"ID":2883856,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.08157","arxiv_id":"2508.08157","title":"Time-delayed opinion dynamics with leader-follower interactions: consensus, stability, and mean-field limits","abstract":"We study a time-delayed variant of the Hegselmann-Krause opinion formation model featuring a small group of leaders and a large group of non-leaders. In this model, leaders influence all agents but only interact among themselves. At the same time, non-leaders update their opinions via interactions with their peers and the leaders, with time delays accounting for communication and decision-making lags. We prove the exponential convergence to consensus of the particle system, without imposing smallness assumptions on the delay parameters. Furthermore, we analyze the mean-field limit in two regimes: (i) with a fixed number of leaders and an infinite number of non-leaders, and (ii) with both populations tending to infinity, obtaining existence, uniqueness, and exponential decay estimates for the corresponding macroscopic models.","short_abstract":"We study a time-delayed variant of the Hegselmann-Krause opinion formation model featuring a small group of leaders and a large group of non-leaders. In this model, leaders influence all agents but only interact among themselves. At the same time, non-leaders update their opinions via interactions with their peers and...","url_abs":"https://arxiv.org/abs/2508.08157","url_pdf":"https://arxiv.org/pdf/2508.08157v1","authors":"[\"Young-Pil Choi\",\"Chiara Cicolani\",\"Cristina Pignotti\"]","published":"2025-08-11T16:32:18Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}