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

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.

19 pages including references

Cited by in corpus (1)

• On the Mean-Field limit of diffusive games through the master equation: $L^{\infty }$ estimates and extreme value behavior