Scaling limit for interacting Ornstein-Uhlenbeck processes
The hydrodynamic scaling limit for a system of interacting particles diffusing on a circle, which was established in the paper reviewed above, is here extended to the case of interacting Ornstein-Uhlenbeck processes. One complication that arises is that the generator of the process of positions and velocities is not symmetric with respect to the equilibrium distribution. It is proved that, as in the above mentioned article, the density of particles in the hydrodynamic limit evolves deterministically in accordance with a nonlinear diffusion equation.
interacting Ornstein- Uhlenbeck processes
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