05/06/2024, 17:00 — 18:00 — Online
Kavita Ramanan, Brown University
Quenched Hydrodynamic Limits for Interacting Jump Processes on Sparse Random Graphs
We consider large systems of jump processes that interact locally with respect to an underlying (possibly random) graph. Such processes model diverse phenomena including the spread of diseases, opinion dynamics and gas dynamics. Under a broad set of assumptions, we show that the empirical measure satisfies a large deviation principle in the sparse regime, that is, when the sequence of graphs converges locally to a limit graph. As a corollary we establish (quenched) hydrodynamic limits for the sequence of interacting jump processes. In addition, for a sub-class of processes that include the SIR process, we obtain a fairly explicit characterization of this limit and provide numerical evidence to show that it serves as a good approximation for finite systems of moderate size.
This is based on various joint works with I-Hsun Chen, Juniper Cocomello and Sarath Yasodharan.
