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We present a proof showing that the weak error of a system of $n$ interactingstochastic particles approximating the solution of the McKean-Vlasov equationis $\mathcal O(n^{-1})$. Our proof is based on the Kolmogorov backward equationfor the particle system and bounds on the derivatives of its solution, which wederive more generally using the variations of the stochastic particle system.The convergence rate is verified by numerical experiments, which also indicatethat the assumptions made here and in the literature can be relaxed.

Weak convergence analysis in the particle limit of the McKean--Vlasov equations using stochastic flows of particle systems