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April 2004 Zero temperature limit for interacting Brownian particles. I. Motion of a single body
Tadahisa Funaki
Ann. Probab. 32(2): 1201-1227 (April 2004). DOI: 10.1214/009117904000000180


We consider a system of interacting Brownian particles in ℝd 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.


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Tadahisa Funaki. "Zero temperature limit for interacting Brownian particles. I. Motion of a single body." Ann. Probab. 32 (2) 1201 - 1227, April 2004.


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

zbMATH: 1121.82028
MathSciNet: MR2060296
Digital Object Identifier: 10.1214/009117904000000180

Primary: 60K35
Secondary: 82C22

Keywords: crystallization , Interacting Brownian particles , rigidity , Scaling limit , zero temperature limit

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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