Propagation of chaos for maxima of particle systems with mean-field drift interaction

Abstract We study the asymptotic behavior of normalized maxima real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation chaos: in large population limit, behave as those arising an i.i.d. system where each particle follows associated McKean–Vlasov limiting dynamics. Because maximum depends on all particles, our does not follow from classical chaos, convergence to limit holds for any fixed number but simultaneously. The proof uses a change measure argument that delicate combinatorial analysis iterated stochastic integrals appearing chaos expansion Radon–Nikodym density.