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April 2004 Zero temperature limit for interacting Brownian particles. II. Coagulation in one dimension
Tadahisa Funaki
Ann. Probab. 32(2): 1228-1246 (April 2004). DOI: 10.1214/009117904000000199


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.


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Tadahisa Funaki. "Zero temperature limit for interacting Brownian particles. II. Coagulation in one dimension." Ann. Probab. 32 (2) 1228 - 1246, April 2004.


Published: April 2004
First available in Project Euclid: 18 May 2004

zbMATH: 1122.82029
MathSciNet: MR2060297
Digital Object Identifier: 10.1214/009117904000000199

Primary: 60K35
Secondary: 82C22

Keywords: coagulation , Interacting Brownian particles , zero temperature limit

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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