{
  "id": "2210.02934",
  "version": "v1",
  "published": "2022-10-06T14:06:26.000Z",
  "updated": "2022-10-06T14:06:26.000Z",
  "title": "Large population limits of Markov processes on random networks",
  "authors": [
    "Marvin Lücke",
    "Jobst Heitzig",
    "Péter Koltai",
    "Nora Molkenthin",
    "Stefanie Winkelmann"
  ],
  "categories": [
    "math.PR"
  ],
  "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 Erd\\H{o}s-R\\'enyi 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-06T14:06:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large population limit",
      "random networks",
      "markov processes",
      "mean-field ordinary differential equation",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}