Thermodynamic limit of interacting particle systems over dynamical networks

The main result presented in this paper (whose proof can be found in [1]) is that the fraction of agents (Y^N<inf>k</inf>(t)) at state k ∊ X := {1, …, K} associated with an interacting particle system over an appropriate dynamical communication network converges weakly to the solution of a differential equation. The vector macroprocess (Y^N(t)) = (Y^N<inf>1</inf>(t),…, Y^N<inf>k</inf>(t)) is not Markov since its evolution depends not only on its current state, but on finer real-time microscopic high-dimensional information of the system — namely, the state of the N nodes X^N(t) ∊ X^N. Our result essentially states that under an appropriate dynamics of the underlying network of contacts, the macroprocess (Y^N(t)) becomes asymptotically (in N) Markov.