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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.
Reviewer: Reviewer (Berlin)
##### MSC:
 82C22 Interacting particle systems in time-dependent statistical mechanics
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##### References:
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