In this talk, we consider interacting particle systems driven by jump processes on sparse graphs. We establish a tractable autonomous description of the dynamics of a vertex and its neighborhood on a unimodular Galton-Watson tree by showing that a Markovian version of the local-field equations is exact under certain conditions on the state space of the dynamics. After presenting the local-field framework as an alternative to mean-field approximations on sparse graphs, we will discuss a few key ideas from the proof and provide examples and simulations to illustrate our results.
The talk is based on joint work with Juniper Cocomello and Kavita Ramanan.
