The Annals of Probability

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

Tadahisa Funaki

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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.

Article information

Source
Ann. Probab., Volume 32, Number 2 (2004), 1228-1246.

Dates
First available in Project Euclid: 18 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1084884850

Digital Object Identifier
doi:10.1214/009117904000000199

Mathematical Reviews number (MathSciNet)
MR2060297

Zentralblatt MATH identifier
1122.82029

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35]

Keywords
Interacting Brownian particles zero temperature limit coagulation

Citation

Funaki, Tadahisa. Zero temperature limit for interacting Brownian particles. II. Coagulation in one dimension. Ann. Probab. 32 (2004), no. 2, 1228--1246. doi:10.1214/009117904000000199. https://projecteuclid.org/euclid.aop/1084884850


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References

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