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

Nikolaos Kolliopoulos (), Martin Larsson () and Zeyu Zhang ()
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Nikolaos Kolliopoulos: University of Michigan
Martin Larsson: Carnegie Mellon University
Zeyu Zhang: Carnegie Mellon University

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-22

Abstract: 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.

Keywords: Mean-field; Propagation of chaos; Order statistics; Extreme value theory; SDE; Interacting diffusions; 60K35; 60H10; 60F05; 60G70 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01397-3

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