  The one-dimensional motion of any number $\cN$ of particles in the field of
many independent waves (with strong spatial correlation) is formulated as a
second-order system of stochastic differential equations, driven by two Wiener
processes. In the limit of vanishing particle mass ${\mathfrak{m}} \to 0$, or
equivalently of large noise intensity, we show that the momenta of all $N$
particles converge weakly to $N$ independent Brownian motions, and this
convergence holds even if the noise is periodic. This justifies the usual
application of the diffusion equation to a family of particles in a unique
stochastic force field. The proof rests on the ergodic properties of the
relative velocity of two particles in the scaling limit.
