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