Creation of chaos for a mean-field model

The article deals with the propagation of chaos for a system of interacting particles. Under suitable assumptions, if the system at time t=0 is chaotic (that is to say the particles are independent), this chaos propagates as the number of particles goes to infinity. Here, we deal with a case in which the system at time t=0 is not chaotic and we show under easily checked assumptions that the system becomes chaotic as the number of particles goes to infinity together with the time. This yields the first result of this type for mean field particle diffusion models