### 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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Zero temperature limit for interacting Brownian particles. I. Motion of a single body.** / Funaki, Tadahisa.

Research output: Contribution to journal › Article

*Annals of Probability*, vol. 32, no. 2, pp. 1201-1227. https://doi.org/10.1214/009117904000000180

}

TY - JOUR

T1 - Zero temperature limit for interacting Brownian particles. I. Motion of a single body

AU - Funaki, Tadahisa

PY - 2004/4

Y1 - 2004/4

N2 - 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.

AB - 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.

KW - Crystallization

KW - Interacting Brownian particles

KW - Rigidity

KW - Scaling limit

KW - Zero temperature limit

UR - http://www.scopus.com/inward/record.url?scp=3042587558&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042587558&partnerID=8YFLogxK

U2 - 10.1214/009117904000000180

DO - 10.1214/009117904000000180

M3 - Article

VL - 32

SP - 1201

EP - 1227

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 2

ER -