Large population limits of Markov processes on random networks
Probability
2026-03-19 v2
Abstract
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called ``voter model'' on Erd\H{o}s-R\'enyi random graphs, on the stochastic block model, and on random regular graphs. Moreover, a heterogeneous population of agents is studied.
Keywords
Cite
@article{arxiv.2210.02934,
title = {Large population limits of Markov processes on random networks},
author = {Marvin Lücke and Jobst Heitzig and Péter Koltai and Nora Molkenthin and Stefanie Winkelmann},
journal= {arXiv preprint arXiv:2210.02934},
year = {2026}
}