Thermodynamic limit of interacting particle systems over dynamical networks
Santos, A. S.
; Kar, S.
; Moura, J.
; Xavier, J.
Thermodynamic limit of interacting particle systems over dynamical networks, Proc The 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, California, United States, Vol. , pp. - , November, 2016.
Digital Object Identifier: 10.1109/ACSSC.2016.7869517
Abstract
The main result presented in this paper (whose proof can be found in [1]) is that the fraction of agents (Y̅ N k (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 (Y̅ N (t)) = (Y̅ N 1 (t),..., Y̅ N k (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 (Y̅ N (t)) becomes asymptotically (in N) Markov.