### Abstract

We consider a system of interacting Brownian particles in ℝ ^{d} with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes a > 0. The asymptotic behavior of the system is studied under the zero temperature limit from both microscopic and macroscopic aspects. If the system is rigidly crystallized, namely if the particles are rigidly arranged in an equal distance a, the crystallization is kept under the evolution in macroscopic time scale. Then, assuming that the crystal has a definite limit shape under a macroscopic spatial scaling, the translational and rotational motions of such shape are characterized.

Original language | English |
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Pages (from-to) | 1201-1227 |

Number of pages | 27 |

Journal | Annals of Probability |

Volume | 32 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 Apr 1 |

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### Keywords

- Crystallization
- Interacting Brownian particles
- Rigidity
- Scaling limit
- Zero temperature limit

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty