Large population limits of Markov processes on random networks

Lücke, Marvin; Heitzig, Jobst; Koltai, Péter; Molkenthin, Nora; Winkelmann, Stefanie

doi:10.1016/j.spa.2023.09.007

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Large population limits of Markov processes on random networks

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Lücke, Marvin
External Organizations;

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Heitzig, Jobst
Potsdam Institute for Climate Impact Research;

Koltai, Péter
External Organizations;

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Molkenthin, Nora
Potsdam Institute for Climate Impact Research;

Winkelmann, Stefanie
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Lücke, M., Heitzig, J., Koltai, P., Molkenthin, N., Winkelmann, S. (2023): Large population limits of Markov processes on random networks. - Stochastic Processes and their Applications, 166, 104220.
https://doi.org/10.1016/j.spa.2023.09.007

Cite as: https://publications.pik-potsdam.de/pubman/item/item_28784

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 Erdős–Rényi random graphs, on the stochastic block model, and on random regular graphs. Moreover, a heterogeneous population of agents is studied.