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Ornstein-Uhlenbeck limit for the velocity process of an \(N\)-particle system interacting stochastically. (English) Zbl 1292.82026
Summary: 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.
MSC:
82C22 Interacting particle systems in time-dependent statistical mechanics
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