Speaker
Description
Traditional models of interacting particle systems often assume a fixed network of connections, which simplifies analysis but fails to capture the dynamics of many real-world phenomena. Consequently, co-evolutionary network models, where the network structure and particle states evolve in mutual influence, are increasingly recognised as essential in diverse fields. For instance, in neuroscience, where learning is encoded through the strengthening and weakening of synaptic connections
(synaptic plasticity). Similarly, in social sciences, the co-evolution
of opinions and social ties is a key driver of social dynamics.
This presentation discusses the rigorous derivation of the mean-field
limit for systems of interacting diffusions on co-evolutionary networks. While previous research has primarily addressed continuum limits or systems with linear weight dynamics, our work overcomes these restrictions. The main challenge arises from the coupling between the network weight dynamics and the agent states, which results in non-Markovian dynamics where the system’s future depends on its entire history. Consequently, the mean-field limit is not described by a partial differential equation, but by a non-Markovian stochastic
integrodifferential equation.
