Large population limits of Markov processes on random networks
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918394153926656 |
|---|---|
| author | Lücke, Marvin Heitzig, Jobst Koltai, Péter Molkenthin, Nora Winkelmann, Stefanie |
| author_facet | Lücke, Marvin Heitzig, Jobst Koltai, Péter Molkenthin, Nora Winkelmann, Stefanie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02934 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Large population limits of Markov processes on random networks Lücke, Marvin Heitzig, Jobst Koltai, Péter Molkenthin, Nora Winkelmann, Stefanie Probability 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. |
| title | Large population limits of Markov processes on random networks |
| topic | Probability |
| url | https://arxiv.org/abs/2210.02934 |