Olla, Stefano; Varadhan, S. R. S. Scaling limit for interacting Ornstein-Uhlenbeck processes. (English) Zbl 0725.60086 Commun. Math. Phys. 135, No. 2, 355-378 (1991). 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. Reviewer: F.Papangelou (Manchester) Cited in 1 ReviewCited in 15 Documents MSC: 60J60 Diffusion processes 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:hydrodynamic scaling limit; interacting particles; interacting Ornstein- Uhlenbeck processes; nonlinear diffusion equation Citations:Zbl 0725.60085 × Cite Format Result Cite Review PDF Full Text: DOI Euclid 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 · doi:10.1002/cpa.3160380611 [4] Varadhan, S.R.S.: Scaling limits for interacting diffusions. Commun. Math. Phys.135, 313–353 (1991) · Zbl 0725.60085 · doi:10.1007/BF02098046 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.