### Abstract

The problem of describing the bulk behavior of an interacting system consisting of a large number of particles comes up in different contexts. See for example [1] for a recent exposition. In [4] one of the authors considered the case of interacting diffusions on a circle and proved that the density of particles evolves according to a nonlinear diffusion equation. The interacting particles evolved according to a generator that was symmetric in equilibrium. In this article we consider interacting Ornstein-Uhlenbeck processes. Here the diffusion generator is not symmetric relative to the equilibrium and the earlier methods have to be modified considerably. We use some ideas that were employed in [3] to extend the central limit theorem from the symmetric to nonsymmetric cases.

Original language | English (US) |
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Pages (from-to) | 355-378 |

Number of pages | 24 |

Journal | Communications In Mathematical Physics |

Volume | 135 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1991 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications In Mathematical Physics*,

*135*(2), 355-378. https://doi.org/10.1007/BF02098047