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