### Abstract

We consider a system of interacting diffusions. The variables are to be thought of as charges at sites indexed by a periodic one-dimensional lattice. The diffusion preserves the total charge and the interaction is of nearest neighbor type. With the appropriate scaling of lattice spacing and time, a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density.

Original language | English (US) |
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Pages (from-to) | 31-59 |

Number of pages | 29 |

Journal | Communications In Mathematical Physics |

Volume | 118 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1988 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Guo, M. Z., Papanicolaou, G. C., & Varadhan, S. R. S. (1988). Nonlinear diffusion limit for a system with nearest neighbor interactions.

*Communications In Mathematical Physics*,*118*(1), 31-59. https://doi.org/10.1007/BF01218476