  Von Renesse and the author (Ann. Prob. '09) developed a second order calculus
on the Wasserstein space P([0,1]) of probability measures on the unit interval.
The basic objects of interest had been Dirichlet form, semigroup and continuous
Markov process, called Wasserstein diffusion. The goal of this paper is to
derive approximations of these objects on the infinite dimensional space P([0,
1]) in terms of appropriate objects on finite dimensional spaces. In
particular, we will approximate the Wasserstein diffusion in terms of
interacting systems of Brownian motions.
