A system of interacting particles described by stochastic differential
equations is considered. As oppopsed to the usual model, where the noise
perturbations acting on different particles are independent, here the particles
are subject to the same space-dependent noise, similar to the (noninteracting)
particles of the theory of diffusion of passive scalars. We prove a result of
propagation of chaos and show that the limit PDE is stochastic and of inviscid
type, as opposed to the case when independent noises drive the different
particles.Comment: Published at http://dx.doi.org/10.1214/15-AAP1120 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
