### Abstract

We study the zero temperature limit for interacting Brownian particles in one dimension with a pairwise potential which is of finite range and attains a unique minimum when the distance of two particles becomes a > 0. We say a chain is formed when the particles are arranged in an "almost equal" distance a. If a chain is formed at time 0, so is for positive time as the temperature of the system decreases to 0 and, under a suitable macroscopic space-time scaling, the center of mass of the chain performs the Brownian motion with the speed inversely proportional to the total mass. If there are two chains, they independently move until the time when they meet. Then, they immediately coalesce and continue the evolution as a single chain. This can be extended for finitely many chains.

Original language | English |
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Pages (from-to) | 1228-1246 |

Number of pages | 19 |

Journal | Annals of Probability |

Volume | 32 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 Apr |

Externally published | Yes |

### Fingerprint

### Keywords

- Coagulation
- Interacting Brownian particles
- Zero temperature limit

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

**Zero temperature limit for interacting Brownian particles. II. Coagulation in one dimension.** / Funaki, Tadahisa.

Research output: Contribution to journal › Article

*Annals of Probability*, vol. 32, no. 2, pp. 1228-1246. https://doi.org/10.1214/009117904000000199

}

TY - JOUR

T1 - Zero temperature limit for interacting Brownian particles. II. Coagulation in one dimension

AU - Funaki, Tadahisa

PY - 2004/4

Y1 - 2004/4

N2 - We study the zero temperature limit for interacting Brownian particles in one dimension with a pairwise potential which is of finite range and attains a unique minimum when the distance of two particles becomes a > 0. We say a chain is formed when the particles are arranged in an "almost equal" distance a. If a chain is formed at time 0, so is for positive time as the temperature of the system decreases to 0 and, under a suitable macroscopic space-time scaling, the center of mass of the chain performs the Brownian motion with the speed inversely proportional to the total mass. If there are two chains, they independently move until the time when they meet. Then, they immediately coalesce and continue the evolution as a single chain. This can be extended for finitely many chains.

AB - We study the zero temperature limit for interacting Brownian particles in one dimension with a pairwise potential which is of finite range and attains a unique minimum when the distance of two particles becomes a > 0. We say a chain is formed when the particles are arranged in an "almost equal" distance a. If a chain is formed at time 0, so is for positive time as the temperature of the system decreases to 0 and, under a suitable macroscopic space-time scaling, the center of mass of the chain performs the Brownian motion with the speed inversely proportional to the total mass. If there are two chains, they independently move until the time when they meet. Then, they immediately coalesce and continue the evolution as a single chain. This can be extended for finitely many chains.

KW - Coagulation

KW - Interacting Brownian particles

KW - Zero temperature limit

UR - http://www.scopus.com/inward/record.url?scp=3042684663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042684663&partnerID=8YFLogxK

U2 - 10.1214/009117904000000199

DO - 10.1214/009117904000000199

M3 - Article

VL - 32

SP - 1228

EP - 1246

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 2

ER -