TY - JOUR
A1 - Lücke, Marvin
A1 - Heitzig, Jobst
A1 - Koltai, Péter
A1 - Molkethin, Nora
A1 - Winkelmann, Stefanie
T1 - Large population limits of Markov processes on random networks
T2 - Stochastic Processes and their Applications
N2 - 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.
Y1 - 2023
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/8790
VL - 166
ER -