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Propagation of Chaos for Point Processes Induced by Particle Systems with Mean-Field Drift Interaction

Author

Listed:
  • Nikolaos Kolliopoulos

    (University of Michigan)

  • Martin Larsson

    (Carnegie Mellon University)

  • Zeyu Zhang

    (Carnegie Mellon University)

Abstract

We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: It has the same weak limit as the point process induced by i.i.d. copies of the solution of a limiting McKean–Vlasov equation. This weak limit is a Poisson point process whose intensity measure is related to classical extreme value distributions. In particular, this yields the limiting distribution of the normalized upper order statistics.

Suggested Citation

  • Nikolaos Kolliopoulos & Martin Larsson & Zeyu Zhang, 2025. "Propagation of Chaos for Point Processes Induced by Particle Systems with Mean-Field Drift Interaction," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-22, March.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01397-3
    DOI: 10.1007/s10959-024-01397-3
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