  An $N$-particle system with stochastic interactions is considered.
Interactions are driven by a Brownian noise term and total energy conservation
is imposed. The evolution of the system, in velocity space, is a diffusion on a
$(3N-1)$-dimensional sphere with radius fixed by the total energy. In the
$N\rightarrow\infty$ limit, a finite number of velocity components are shown to
evolve independently and according to an Ornstein-Uhlenbeck process.
