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Scaling limit for interacting Ornstein-Uhlenbeck processes. (English) Zbl 0725.60086

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.

MSC:

60J60 Diffusion processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory

Citations:

Zbl 0725.60085
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References:

[1] Deuschel, J.D., Stroock, D.W.: Large deviations. New York: Academic Press 1989 · Zbl 0705.60029
[2] De Masi, A., Presutti, E.: Lectures on the collective behavior of particle systems. C.A.R.R. Reports in Mathematical Physics, 5/89, 1989
[3] Papanicolaou, G., Varadhan, S.R.S.: Ornstein-Uhlenbeck process in a random potential. Commun. Pure Appl. Math.35, 819–834 (1985) · Zbl 0617.60078
[4] Varadhan, S.R.S.: Scaling limits for interacting diffusions. Commun. Math. Phys.135, 313–353 (1991) · Zbl 0725.60085
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