| Abstract: |
| A central distinction in interacting particle systems is between indistinguishable and non-exchangeable cases. In the latter, particle identity plays a key role, and interactions are naturally modeled by systems of ODEs on weighted graphs. In this talk, we study such systems and their large-population behavior, highlighting the connection between graph limit and mean-field approaches.
Our main focus is on systems evolving on adaptive dynamical networks, where agents interact through weighted graphs whose structure evolves over time in a coupled manner with the agents' states. In the dense-graph regime, we show that the large-population limit is described by a Vlasov-type equation posed on an extended phase space including agent states, identities, and evolving interaction weights.
We present two complementary derivations of this limit: a mean-field approach in the spirit of Sznitman's work, under a structural assumption on the weight dynamics, and a deterministic graph limit approach that allows us to remove this restriction. |
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