We will report on the paper  “On the McKean-Vlasov limit for interacting diffusions” by Gärtner. In this talk, we first describe a weakly interacting N-particle system, in which particle moves according to a diffusion with diffusion matrix and drift vector. We know that the stochastic evloution of this system can be described by a solution to a martingale problem. Then we want to prove the uniqueness of the nonlinear martingale problem, which results in the uniqueness of the weak solution of the McKean-Vlasov equation. Finally, we study the evolution of a fixed number of test particles in the N-particle system with N tending to infinity.

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