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

Bruno Vieira Ribeiro, Yves Elskens
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 $N'\to\infty$ limit, a finite number of velocity components are shown to evolve independently and according to an Ornstein-Uhlenbeck process.
View original: http://arxiv.org/abs/1304.4034