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We study the $N \to \infty$ limit of the normalized largest component in somesystems of $N$ diffusive particles with mean-field interaction. By applying auniversal time change, the interaction in noises is transferred to the driftterms, and the asymptotic behavior of the maximum becomes well-understood dueto existing results in the literature. We expect that the normalized maximum inthe original setting has the same limiting distribution as that of i.i.d copiesof a solution to the corresponding McKean-Vlasov SDE and we present someresults and numerical simulations that support this conjecture.

Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises