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Large population limits of Markov processes on random networks

Title data

Lücke, Marvin ; Heitzig, Jobst ; Koltai, Peter ; Molkenthin, Nora ; Winkelmann, Stefanie:
Large population limits of Markov processes on random networks.
In: Stochastic Processes and their Applications. Vol. 166 (2023) . - 104220.
ISSN 0304-4149
DOI: https://doi.org/10.1016/j.spa.2023.09.007

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data > Chair Dynamical Systems and Data - Univ.-Prof. Dr. Peter Koltai
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 11 Jan 2023 11:03
Last Modified: 13 Nov 2023 10:25
URI: https://eref.uni-bayreuth.de/id/eprint/73176