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We study the asymptotic behavior of the normalized maxima of real-valueddiffusive particles with mean-field drift interaction. Our main resultestablishes propagation of chaos: in the large population limit, the normalizedmaxima behave as those arising in an i.i.d. system where each particle followsthe associated McKean--Vlasov limiting dynamics. Because the maximum depends onall particles, our result does not follow from classical propagation of chaos,where convergence to an i.i.d. limit holds for any fixed number of particlesbut not all particles simultaneously. The proof uses a change of measureargument that depends on a delicate combinatorial analysis of the iteratedstochastic integrals appearing in the chaos expansion of the Radon--Nikodymdensity.

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