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arXiv · 2303.11426

Propagation of chaos for point processes induced by particle systems with mean-field drift interaction

Nikolaos Kolliopoulos·Martin Larsson·Zeyu Zhang
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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.

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Nikolaos Kolliopoulos, Martin Larsson, Zeyu Zhang. 2023-03-20. Propagation of chaos for point processes induced by particle systems with mean-field drift interaction. https://doi.org/10.1007/s10959-024-01397-3

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