Abstract

We consider interacting particle systems on suitable convergent sequences of sparse (or heterogeneous graphs) and show that the limiting dynamics of the associated neighborhood empirical measure process
(the so-called hydrodynamic limit) can be autonomously characterized in terms of a non-Markovian process.   We then describe Markovian approximations to the latter and provide examples where they are exact.   This includes joint work with G. Cocomello and A. Ganguly.