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An $N$-particle system with stochastic interactions is considered.Interactions are driven by a Brownian noise term and total energy conservationis 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 toevolve independently and according to an Ornstein-Uhlenbeck process.

Ornstein-Uhlenbeck limit for the velocity process of an $N$-particle system interacting stochastically