8790
2023
eng
166
article
0
2023-09-20
2023-09-30
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Large population limits of Markov processes on random networks
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, as well as on random regular graphs. Moreover, a heterogeneous population of agents is studied. For each of these types of interaction networks, we specify the convergence conditions in dependency on the corresponding model parameters.
Stochastic Processes and their Applications
10.1016/j.spa.2023.09.007
2210.02934
publish
yes
2023-09-13
Marvin Lücke
Stefanie Winkelmann
Jobst Heitzig
Péter Koltai
Nora Molkethin
Stefanie Winkelmann
Numerical Mathematics
Computational Systems Biology
Winkelmann, Stefanie
Modeling and Simulation of Complex Processes
Lücke, Marvin
MathPlusEF4-8